Tension in post-tensioned rods

ABSTRACT

A system for estimating tension in a post-tensioned rod is provided. The system includes an impact device for transversely-impacting a post-tensioned rod, an accelerometer configured to generate data indicative of a vibrational response in the post-tensioned rod, and a receiver communicatively coupled to the accelerometer. The receiver includes a display, at least one input device, a communication module, a processor, and one or more memory devices coupled to the processor. Instructions stored on the one or more memory devices, when executed by the processor, cause the processor to receiver the data indicative of a vibrational response in the post-tensioned rod, process the received data to determine a difference between a first and a second modal frequency corresponding to the vibrational response, and store the difference between a first and second modal frequency corresponding to the vibrational response. The receiver is configured to transmit the stored difference between a first and second modal frequency.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of U.S. application Ser. No.17/432,341 filed on Aug. 19, 2021 and titled “Tension in Post-TensionedRods,” which is a U.S. national stage application under § 371 ofInternational Patent Application No. PCT/US2020/059495, filed Nov. 6,2020, which claims the benefit under 35 U.S.C. § 119(e) of the followingU.S. provisional patent applications: U.S. Provisional PatentApplication Ser. No. 62/931,671 filed Nov. 6, 2019 and titled “Systemsand Methods for Estimating Tension in Post-Tensioned Rods”; U.S.Provisional Patent Application Ser. No. 62/931,673 filed Nov. 6, 2019and titled “Systems and Methods for Modeling Tension in Post-TensionedRods”; U.S. Provisional Patent Application Ser. No. 62/933,737 filedNov. 11, 2019 and titled “Systems and Methods for Estimating Tension inPost-Tensioned Rods Using Signal Damping”; U.S. Provisional PatentApplication Ser. No. 62/931,675 filed Nov. 6, 2019 and titled “Apparatusand Methods for Orienting a Measuring Device on Post-Tensioned Rods”;and U.S. Provisional Patent Application Ser. No. 62/931,662 filed Nov.6, 2019 and titled “Computer-Implemented Systems and Methods forDetermining Modal Frequencies of Post-Tensioned Rods.” The disclosuresof all above-identified applications are expressly incorporated hereinby reference in their entireties and are hereby made a part of thisspecification.

TECHNICAL FIELD

The present disclosure generally relates to evaluating tension inpost-tensioned rods. More specifically, the present disclosure relatesto systems, methods, and apparatuses for estimating, determining, and/orpredicting tension in post-tensioned rods, such as anchor rods used tosupport structures.

BACKGROUND

Rods are used in structural systems for strength and stability. One typeof rod is an anchor rod used to anchor structural steel to concrete(sometimes referred to as an “anchor bolt”). Depending on designconsiderations and constraints, anchor rods may be pre- orpost-tensioned. An anchor rod can be pre-tensioned by imparting tensileforces onto the rod before embedding it within concrete, then allowingthe concrete to set and to bond to the rod. Once the concrete sets andthe ends of the rod are released, the tension in the rod is transferredinto the concrete. Alternatively, an anchor rod can be post-tensioned byfirst embedding the rod in concrete, then applying tension after theconcrete sets. For post-tensioned anchor rods, the rods are typicallyencased within a sheath in the concrete, such as in a PVC sleeve, toprevent the rod from bonding to the concrete. Instead of bonding, oneend of the rod is fastened to an anchor assembly in the concrete whilethe other end of the rod remains outside, which can be used to anchor astructure.

FIG. 1 is a partial front elevation view illustrating an anchor rod 110embedded in a concrete foundation 120. As illustrated, anchor rod 110 isencased within sheath 106 and clamped to the bottom anchor plate 102with nuts 114. As further illustrated, an un-tensioned portion of therod, cantilever 112, remains above anchor plate 102 and outside ofconcrete foundation 120. Once the concrete sets, cantilever 112 can beused to anchor a structure to the concrete foundation 120. An exampleapplication for anchor rod 110 is illustrated in FIG. 2 , which is aperspective view of an anchor cage 100 that may be used to secure anonshore wind turbine to a concrete foundation 120. The entire anchorcage 100 would be embedded in a concrete foundation (not shown) with thetwo concentric rings of cantilevers 112 remaining above the concrete.Flanges on the base of a wind turbine would be placed on top of plate104 and over cantilevers 112. An inside flange would be secured to theinner ring of cantilevers 112, while an outside flange would be securedto the outer ring of cantilevers 112. This is illustrated in FIG. 3 ,which is a partial view of anchor cage 100 after it has been embedded ina concrete foundation 120. As illustrated, outside flange 132 of windturbine tower 130 is placed over the outer ring of cantilevers 112 andsecured to the concrete foundation 120 with nuts 114.

The foregoing description is merely one example of post-tensioned rods.Post-tensioned rods can be used for structural support in manyapplications including, for example, wind turbines, communicationtowers, power transmission towers, light poles, rock anchors, buildings,bridges, dams, etc. In many circumstances, it is desirable to determineor estimate the amount of tension in a post-tensioned rod in situ. Forexample, to ensure that a structure does not collapse or tip over,engineers specify a tension to which an anchor rod must be set. For bothsafety and insurance purposes, the tension in anchor rods areperiodically audited to ensure that the rods have not loosened overtime, i.e., have a tension below the specified design tension.

One known method for auditing tension in post-tensioned rods is referredto as a “lift-off” method. This method requires applying an increasingload to the cantilevers of anchor rods until the point when the securingnut “lifts off” and becomes loose. At the point of lift-off, tension inthe loaded cantilever will be substantially equal to tension in theanchor rod below the concrete. It can then be determined whether theloaded tension meets the specified design tension and, if not, the nuton the cantilever can be tightened at the specified tension. This methodposes serious safety concerns and may not always work as intended. Forone, it requires the use of heavy machinery, such as a hydraulic jack,which may not be easy or feasible to bring to a worksite and requiresmultiple people to operate. Moreover, if any anomalies exist in theanchor rod, such as cracks or corrosion, the rod can break duringloading, potentially leading to a catastrophic collapse of thestructure. Rust is another factor that can complicate matters. Asexplained above, anchor rods used to secure a structure typically remainexposed to the elements. Consequently, the exposed anchor rods and nutsinevitably rust over time. The rust can be so pervasive that the nut maynot lift-off at all when the method is performed.

The lift-off method is also inefficient and time-consuming. For example,in the case of post-tensioned rods used to secure the base of a windturbine to a concrete foundation, there can be as many as 120, 140, 200or more anchor rods that secure the wind turbine. In practice, crews areoften tasked with auditing the tension in about 10% of the anchor rodsaround the outside perimeter of the wind turbine base. Performing thelift-off method for each anchor rod requires at least two people and cantake up to fifteen minutes or more for each rod. If the crew finds thateven one of the audited rods has a tension below the specified designtension, the crew will typically test and tighten every remaining anchorrod. Consequently, it can take up to several days or more to audit thetension in anchor rods for just one structure. Considering that a windfarm can include numerous wind turbines (e.g., up to 100 or more), thelift-off method can be exceedingly time-consuming and expensive to audittension in anchor rods. And, the safety concerns noted above areamplified when repeatedly performing the lift-off method for everyanchor rod of every wind turbine at a wind farm. Also, if the tension inthe audited anchor rods meets the specified design tension, critically,results from the lift-off method provide no insight about the tensionfor the remaining anchor rods that were not audited.

A safer and more efficient way of estimating, determining, and/orpredicting tension in post-tensioned rods is therefore needed.

SUMMARY

The present disclosure provides systems, methods, and apparatuses forestimating, determining, and/or predicting tension in post-tensionedrods. The inventive systems, methods, and apparatuses generally involvecreating a model for known tension levels in a subset of post-tensionedrods, then using the model to predict the tension in otherpost-tensioned rods. Because only a subset of post-tensioned rods areused to create the model, many of the safety concerns and inefficienciesof known methods are reduced or eliminated altogether. Indeed, theinventive systems, methods, and apparatuses can be applied to accuratelypredict the tension in all post-tensioned anchor rods at a wind farm ina fraction of the time and for a fraction of the cost of known methods.The inventive systems, methods, and apparatuses are also much safer thanknown methods because once a model is created, only the vibrationalresponses of post-tensioned rods are needed, which are procured in anon-destructive manner. Moreover, knowing the tension in every anchorrod can provide valuable insight for prioritizing which anchor rods toaddress for purposes of complying with design tensions.

In a first aspect, a method of estimating tension in a targetpost-tensioned rod is provided. The method includes modeling tension forthe plurality of post-tensioned rods as a function of frequencydifferences between a first and a second modal frequency and cantileverlength of each rod. The method further includes measuring the length ofa cantilever of the target post-tensioned rod, determining a first modalfrequency of the target post-tensioned rod, determining a second modalfrequency of the target post-tensioned rod, and determining a frequencydifference between the first modal frequency and the second modalfrequency for the target post-tensioned rod. The method further includesestimating tension in the target post-tensioned rod based on at leastthe model.

In an embodiment of the first aspect, the step of modeling tension forthe plurality of post-tensioned rods can include, for eachpost-tensioned rod in the plurality, obtaining a frequency response forone or more levels of tension and recording the length of a cantileverportion at each of the one or more levels of tension. The step canfurther include determining, from the frequency responses for eachpost-tensioned rod, frequency differences between first and second modalfrequencies at each of the one or more levels of tension. The step canfurther include grouping the cantilever lengths into one or more groups.The step can further include performing regression analysis for eachgroup, wherein the regression analysis is based on at least thefrequency differences and the levels of tension.

In an embodiment of the first aspect, the step of obtaining a frequencyresponse for one or more levels of tension can include setting tensionin the post-tensioned rod to one or more levels of tension. The step canfurther include, for each level of tension, detachably coupling anaccelerometer to the cantilever portion of the post-tensioned rod,applying one or more transversely-directed impacts to the cantileverportion of the post-tensioned rod, receiving temporal data from theaccelerometer associated with a vibrational response for each of the oneor more impacts, transforming the temporal data to the frequency domainto obtain a frequency response for each of the one or more impacts,measuring the level of tension in the post-tensioned rod, andassociating a level of tension in the post-tensioned rod with each ofthe one or more frequency responses.

In an embodiment of the first aspect, the step of associating a level oftension in the post-tensioned rod with each of the one or more frequencyresponses can include finding, for each level of tension, an average of(a) the level of tension set in the post-tensioned rod and (b) the levelof tension measured in the post-tensioned rod. The step can furtherinclude associating the average tension with each correspondingfrequency response.

In an embodiment of the first aspect, the step of determining, from thefrequency responses for each post-tensioned rod, frequency differencesbetween first and second modal frequencies at each of the one or morelevels of tension can include, for each level of tension, determining avalue for the first modal frequency from each frequency response forthat level of tension, determining a value for the second modalfrequency from each frequency response for that level of tension,determining an average of the values for the first modal frequency,determining an average of the values for the second modal frequency, anddetermining a frequency difference between the average first modalfrequency and the average second modal frequency.

In an embodiment of the first aspect, the step of grouping thecantilever lengths into one or more groups can include grouping thecantilever lengths into at least four groups.

In an embodiment of the first aspect, the cantilever length group canspan approximately one-half inch.

In an embodiment of the first aspect, the step of determining a firstmodal frequency of the target post-tensioned rod can include detachablycoupling an accelerometer to the cantilever portion of the targetpost-tensioned rod. The step can further include applying one or moretransversely-directed impacts to the cantilever portion of the targetpost-tensioned rod. The step can further include receiving, from theaccelerometer, data associated with a vibrational response for each ofthe one or more impacts. The step can further include determining, fromthe received data, a value for the first modal frequency for each of theone or more impacts, and determining a first modal frequency of thetarget post-tensioned rod based on an average of the values for thefirst modal frequency for the one or more impacts.

In an embodiment of the first aspect, the step of determining a secondmodal frequency of the target post-tensioned rod can include detachablycoupling an accelerometer to the cantilever portion of the targetpost-tensioned rod. The step can further include applying one or moretransversely-directed impacts to the cantilever portion of the targetpost-tensioned rod. The step can further include receiving, from theaccelerometer, data associated with a vibrational response for each ofthe one or more impacts. The step can further include determining, fromthe received data, a value for the second modal frequency for each ofthe one or more impacts, and determining a second modal frequency of thetarget post-tensioned rod based on an average of the values for thesecond modal frequency for the one or more impacts.

In an embodiment of the first aspect, the step of estimating tension inthe target post-tensioned rod based on at least the model can includeidentifying a level of tension in the model that corresponds to thefrequency difference and the length of the cantilever portion of thetarget post-tensioned rod.

In an embodiment of the first aspect, the method can further includedetermining a decay time for the target post-tensioned rod.

In an embodiment of the first aspect, if the frequency difference in thetarget post-tensioned rod corresponds to more than one tension level inthe model, estimating tension in the target post-tensioned rod can befurther based on the decay time.

In an embodiment of the first aspect, the step of estimating tension inthe target post-tensioned rod further based on the decay time caninclude selecting the lowest tension level in the model that correspondsto the frequency difference in the target post-tensioned rod when thedecay time is above a first threshold, and selecting the highest tensionlevel in the model that corresponds to the frequency difference in thetarget post-tensioned rod when the decay time is below the firstthreshold.

In an embodiment of the first aspect, the step of determining a decaytime for the target post-tensioned rod can include detachably couplingan accelerometer to a cantilever portion of the target post-tensionedrod. The step can further include applying one or moretransversely-directed impacts to the cantilever portion of the targetpost-tensioned rod. The step can further include receiving, from theaccelerometer, data associated with a vibrational response for each ofthe one or more impacts. The step can further include determining, fromthe received data, a decay time for each of the one or more impacts,wherein the decay time is the time that it takes the vibrationalresponse to dampen to a second threshold, and determining a decay timefor the target post-tensioned rod based on an average of the decay timesfor the one or more impacts.

In an embodiment of the first aspect, the second threshold can be aboutten percent of the maximum amplitude of the vibrational response.

In a second aspect, a method of estimating tension in a targetpost-tensioned rod is provided. The method includes determiningfrequency differences between first and second modal frequencies for aplurality of post-tensioned rods, wherein the frequency differences aredetermined for each rod at one or more levels of tension, anddetermining a frequency difference between a first and a second modalfrequency for the target post-tensioned rod. The method further includesmeasuring cantilever lengths of the plurality of post-tensioned rods,wherein the cantilever lengths are measured for each rod at one or morelevels of tension, and measuring a cantilever length of the targetpost-tensioned rod. The method further includes applying regressionanalysis to estimate tension in the target post-tensioned rod, whereinthe regression analysis is based on at least the frequency differencesdetermined for the plurality of post-tensioned rods, the frequencydifference for the target post-tensioned rod, the measured cantileverlengths for the plurality of post-tensioned rods, and the measuredcantilever length of the target post-tensioned rod.

In an embodiment of the second aspect, the step of determining frequencydifferences between first and second modal frequencies can includedetachably coupling an accelerometer to a cantilever of a post-tensionedrod. The step can further include applying one or moretransversely-directed impacts to the cantilever. The step can furtherinclude receiving, from the accelerometer, data associated with avibrational response for each of the one or more impacts. The step canfurther include determining, for each of the one or more impacts, that asecond modal frequency can be determined from the received data. Thestep can further include determining, from the received data, a valuefor the first modal frequency corresponding to each impact. The step canfurther include determining, from the received data, a value for thesecond modal frequency corresponding to each impact. The step canfurther include determining, from at least the values for the firstmodal frequency and the values for the second modal frequency, that afrequency difference can be determined for the values of the first andsecond modal frequencies. The step can further include determining afrequency difference between an average of the values for the firstmodal frequency and an average of the values for the second modalfrequency.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining, from atime-domain representation of the received data, that a maximumamplitude is below a threshold.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining, from atime-domain representation of the received data, that noise is below athreshold.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining, from atime-domain representation of the received data, that a minimumamplitude is above a threshold.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining, from atime-domain representation of the received data, that the received datadecays at an exponential rate until steady state.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining, from afrequency-domain representation of the received data, that the sum ofamplitudes of composite frequencies in a range is below a threshold.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining a first modalfrequency from the received data, finding a Fast Fourier Transform (FFT)of a frequency-domain representation of the received data, determining,from the FFT of the frequency-domain representation of the receiveddata, that an amplitude corresponding to the period of the first modalfrequency is less than an amplitude of the received data correspondingto the closest local maxima at a value less than the period of the firstmodal frequency, and determining, from the FFT of the frequency-domainrepresentation of the received data, that the amplitude corresponding tothe period of the first modal frequency is less than an amplitudecorresponding to twice the period of the first modal frequency.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining, from afrequency-domain representation of the received data, that amplitudes ofat least three local maxima have widths at half-peak amplitude that isless than a threshold and amplitudes less than half of the maximumpossible amplitude for the second modal frequency.

In an embodiment of the second aspect, the step of determining, for eachof the one or more impacts, that a second modal frequency can bedetermined from the received data can include determining, from afrequency-domain representation of the received data, that a lowerquartile of amplitudes in a range of frequencies is less than athreshold.

In an embodiment of the second aspect, the step of determining, from thereceived data, a value for the second modal frequency corresponding toeach impact can include identifying a first frequency with the highestamplitude within a first range of frequencies. The step can furtherinclude determining, from the received data, whether a frequency-domainrepresentation of the received data contains peak values at any whole orhalf multiples of a first modal frequency, wherein, if thefrequency-domain representation of the received data does not containpeak values at any whole or half multiples of the first modal frequency,setting a value for the second modal frequency equal to the firstfrequency, and wherein, if the frequency-domain representation of thereceived data contains peak values at any whole or half multiples of thefirst modal frequency, setting the amplitude at the first frequency tozero, and setting a value for the second modal frequency equal to asecond frequency with the highest amplitude within the first range offrequencies.

In an embodiment of the second aspect, the step of determining, from atleast the values for the first modal frequency and the values for thesecond modal frequency, that a frequency difference can be determinedfor the values of the first and second modal frequencies can includeidentifying unique groups of values for the second modal frequency,removing outliers from each unique group of values for the second modalfrequency, determining, from the unique groups, an optimum group,computing, from the optimum group, an average of the values for thesecond modal frequency, removing outliers from the values of the firstmodal frequency, and computing an average of the remaining values forthe first modal frequency.

In an embodiment of the second aspect, the step of identifying uniquegroups of values for the second modal frequency can include defining,for each value for the second modal frequency, a bin window thatcorresponds to the value plus a frequency differential. The step canfurther include defining, for each bin window, a group as comprising allvalues for the second modal frequency that fall within the bin window.The step can further include discarding groups that are fullyencompassed within another group.

In an embodiment of the second aspect, the step of removing outliersfrom each unique group of values for the second modal frequency caninclude discarding each unique group that contains an amount of valuesfor the second modal frequency below a minimum threshold of values. Thestep can further include discarding, for each remaining unique group,any value that is greater than five standard deviations away from anaverage of the remaining values in the group. The step can furtherinclude discarding each remaining unique group that contains an amountof values for the second modal frequency below the minimum threshold ofvalues. The step can further include discarding groups that are fullyencompassed within another group.

In an embodiment of the second aspect, the step of determining, from theunique groups, an optimum group can include computing confidence sumsfor each unique group, and identifying an optimum group as the groupwith the highest confidence sum. If two or more groups have the samehighest confidence sum, the step can further include identifying anoptimum group as the group containing the most number of the highestconfidence level, wherein, if two or more groups have an equal number ofthe highest confidence level, the step can further include identifyingan optimum group as the group containing the most values for the secondmodal frequency, wherein, if two or more groups have an equal number ofvalues for the second modal frequency, the step can further includedetermining that an optimum group cannot be identified.

In a third aspect, a system for estimating tension in a post-tensionedrod is provided. The system includes an impact device fortransversely-impacting a post-tensioned rod, an accelerometer configuredto generate data indicative of a vibrational response in thepost-tensioned rod, and a receiver communicatively coupled to theaccelerometer. The receiver includes a display, at least one inputdevice, a communication module, a processor, and one or more memorydevices coupled to the processor. The one or more memory devices storesinstructions that, when executed by the processor, cause the processorto receive the data indicative of a vibrational response in thepost-tensioned rod, process the received data to determine a differencebetween a first and a second modal frequency corresponding to thevibrational response, and store the difference between a first andsecond modal frequency corresponding to the vibrational response. Thereceiver is configured to transmit to an external system, via thecommunication module, the stored difference between a first and secondmodal frequency.

In a fourth aspect, a computing device for determining a frequencydifference between a first and a second modal frequency of apost-tensioned rod is provided. The computer device includes an inputmodule configured to receive, from an accelerometer detachably coupledto a post-tensioned rod, data resulting from one or more impacts to acantilever portion of the post-tensioned rod, and a processor connectedto the interface. The processor is configured to: determine, for each ofthe one or more impacts, that a second modal frequency can be determinedfrom the received data; determine, from the received data, a value forthe first modal frequency corresponding to each impact; determine, fromthe received data, a value for the second modal frequency correspondingto each impact; determine, from at least the values for the first modalfrequency and the values for the second modal frequency, that afrequency difference can be determined for the values of the first andsecond modal frequencies; and determine the frequency difference betweenan average of the values for the first modal frequency and an average ofthe values for the second modal frequency.

In a fifth aspect, a non-transitory computer readable medium includingcomputer-executable instructions stored thereon, which, when executed bya processor, implement instructions for determining a frequencydifference between a first and second modal frequency of apost-tensioned rod is provided. The instructions include receiving, froman accelerometer detachably coupled to a post-tensioned rod, dataresulting from one or more impacts to a cantilever portion of thepost-tensioned rod; determining, for each of the one or more impact,that a second modal frequency can be determined from the received data;determining, from the received data, a value for the first modalfrequency corresponding to each impact; determining, from the receiveddata, a value for the second modal frequency corresponding to eachimpact; determining, from at least the values for the first modalfrequency and the values for the second modal frequency, that afrequency difference can be determined for the values of the first andsecond modal frequencies; and determining the frequency differencebetween an average of the values for the first modal frequency and anaverage of the values for the second modal frequency.

In a sixth aspect, a method for determining whether a frequencydifference between a first and second modal frequency of apost-tensioned rod can be found is provided. The method includesreceiving, from an accelerometer detachably coupled to a post-tensionedrod, data resulting from one or more impacts to a cantilever portion ofthe post-tensioned rod, and determining, for each of the one or moreimpact, whether a second modal frequency can be determined from thereceived data. If a second modal frequency cannot be determined from thereceived data, the method further includes providing an indication thata frequency difference between a first and second modal frequency of apost-tensioned rod cannot be found from the received data.

In an embodiment of the sixth aspect, the step of providing anindication that a frequency difference between a first and second modalfrequency of a post-tensioned rod cannot be found from the received datacan include sending an error message.

In an embodiment of the sixth aspect, sending an error message caninclude requesting that the cantilever portion of the post-tensioned rodbe struck again.

In a seventh aspect, a computing device for estimating tension in atarget post-tensioned rod is provided. The computing device includes adisplay, an input module configured to receiver data from anaccelerometer detachably coupled to a post-tensioned rod, and aprocessor coupled to the input module and one or more memory devices.The processor is configured to execute instructions stored in the onemore memory devices, wherein execution of the instructions causes agraphical user interface to be displayed on the display, wherein thegraphical user interface is configured to receive input from a user;receive, from the input module, and process, data corresponding tovibrational responses associated with impacting a plurality ofpost-tensioned rods, wherein each impact on each rod in the plurality ofpost-tensioned rods corresponds to a level of tension; receive, from theinput module, and process, data corresponding to a vibrational responseassociated with impacting the target post-tensioned rod; receive, fromthe graphical user interface, and process, data corresponding to lengthsof cantilevers for each rod in the plurality of rods, wherein eachlength of each cantilever corresponds to a level of tension; receive,from the graphical user interface, and process, data corresponding to alength of a cantilever of the target post-tensioned rod; performregression analysis on the data corresponding to vibrational responsesassociated with impacting the plurality of post-tensioned rods, the datacorresponding to a vibrational response associated with impacting thetarget post-tensioned rod, the data corresponding to lengths ofcantilevers for each rod in the plurality of rods, and the datacorresponding to a length of a cantilever of the target post-tensionedrod; and provide an estimate of the tension in the target post-tensionedrod based on at least the regression analysis.

In an eighth aspect, an apparatus for orienting an accelerometer onpost-tensioned rod is provided. The apparatus includes an elongatestructure that includes a first open channel having a first sidewallforming a substantially half cylinder shape along at least a portion ofa length of the first open channel, and a first axis along a length ofthe first open channel; a second open channel having a second sidewallforming a substantially half cylinder shape along at least a portion ofa height of the second open channel, and a second axis along a height ofthe second open channel; and a stopper wall having an inner surfacedisposed internal to a top end of the second channel, said inner surfacebeing substantially perpendicular to the second axis. The apparatusfurther includes the first axis being substantially perpendicular to thesecond axis, and the first and second channels being contiguous.

In an embodiment of the eighth aspect, a distance from a boundarybetween the first open channel and second open channel to the innersurface of the stopper wall can be at least 0.5 inches.

In an embodiment of the eighth aspect, the first open channel can besuitable for receiving, along its length, a cylindrical magnet, anaccelerometer, and a wire coupled to the accelerometer.

In an embodiment of the eighth aspect, the second open channel can besuitable for receiving, along its height, a substantially cylindrical,post-tensioned rod.

In an embodiment of the eighth aspect, a radius of the second sidewallcan be between about 0.5 inch and one inch.

In an embodiment of the eighth aspect, a radius of the second sidewallcan be between about 0.65 inch and 0.85 inch.

In an embodiment of the eighth aspect, the radius of the second sidewallcan be approximately 0.75 inches.

DRAWINGS

The foregoing and other objects, features, and advantages of thesystems, methods, and apparatuses described herein will be apparent fromthe following description of particular embodiments thereof, asillustrated in the accompanying figures, where like reference numbersrefer to like structures. The figures are not necessarily to scale,emphasis instead being placed upon illustrating the principles of thesystems, methods, and apparatuses described herein.

FIG. 1 is a partial front elevation view illustrating an anchor rodembedded in a concrete foundation.

FIG. 2 is a perspective view illustrating an example anchor cage thatmay be used to secure an onshore wind turbine to a concrete foundation.

FIG. 3 is a partial view of the anchor cage of FIG. 2 after it has beenembedded in a concrete foundation.

FIG. 4 is a schematic diagram illustrating an example setup of a systemfor estimating tension in post-tensioned rods.

FIG. 5 is a right-side perspective view illustrating an exampleorienting apparatus.

FIG. 6 is a top perspective view illustrating an example orientingapparatus.

FIG. 7 is a perspective view illustrating a magnet, a sensor, and atransmission line positioned in an example orienting apparatus.

FIG. 8 is a perspective view illustrating an example of an operatorusing an orienting apparatus.

FIG. 9 is a perspective view illustrating a sensor detachably coupled toa cantilever of a post-tensioned rod.

FIG. 10 is a front elevation view illustrating an example orientingapparatus.

FIG. 11 is a right-side elevation view illustrating an example orientingapparatus.

FIG. 12 is a rear elevation view illustrating an example orientingapparatus.

FIG. 13 is a left-side elevation view illustrating an example orientingapparatus.

FIG. 14 is a top plan view illustrating an example orienting apparatus.

FIG. 15 is a bottom plan view illustrating an example orientingapparatus.

FIG. 16 is a right-side perspective view illustrating an exampleorienting apparatus.

FIG. 17 is a side elevation view illustrating a cantilever and nut, andexample locations where a sensor can be detachably coupled and where acantilever can be impacted.

FIG. 18 is a front elevation view illustrating a cantilever and nut, andexample locations where a sensor can be detachably coupled and where acantilever can be impacted.

FIG. 19 is a simplified block diagram illustrating a sensor incommunication with a receiver according to some embodiments.

FIG. 20 is a simplified block diagram illustrating a sensor incommunication with a receiver, and a receiver in communication with anexternal system, according to some embodiments.

FIG. 21 is a block diagram illustrating an example receiver according tosome embodiments.

FIG. 22 is a graph diagram illustrating an example of temporal dataassociated with a vibrational response received from an accelerometer.

FIG. 23 is a graph diagram illustrating an example frequency responseassociated with a vibrational response received from an accelerometer.

FIG. 24 is a graph diagram illustrating example regression plots forfour cantilever groupings.

FIG. 25 is a graph diagram illustrating data associated with avibrational response and a decay time.

FIG. 26 is a flow diagram illustrating an example method for estimatingtension in a target post-tensioned rod.

FIG. 27 is a flow diagram illustrating an example method for modelingtension for a plurality of post-tensioned rods.

FIG. 28 is a flow diagram illustrating an example method for obtaining afrequency response for one or more levels of tension.

FIG. 29 is a flow diagram illustrating an example method for determiningfrequency differences between first and second modal frequencies.

FIG. 30 is a flow diagram illustrating an example method for determininga modal frequency of a target post-tensioned rod.

FIG. 31 is a flow diagram illustrating an example method for determininga decay time for a target post-tensioned rod.

FIG. 32 is a flow diagram illustrating an example method for estimatingtension in a target post-tensioned rod.

FIG. 33 is a flow diagram illustrating an example method for determininga frequency difference between first and second modal frequencies of apost-tensioned rod.

FIG. 34 is a flow diagram illustrating an example method for determiningwhether an impact made to a cantilever is valid.

FIG. 35 is a graph diagram illustrating an example waveform in the timedomain that decays exponentially until steady state.

FIG. 36 is a graph diagram illustrating an example waveform in the timedomain that does not decay exponentially until steady state.

FIG. 37 is a graph diagram illustrating an example waveform in thefrequency domain containing periodic amplitudes.

FIG. 38 is a graph diagram illustrating an FFT of the graph of FIG. 37 .

FIG. 39 is a flow diagram illustrating a general method for determiningwhether an impact is valid.

FIG. 40 is a flow diagram illustrating an example method for determininga second modal frequency.

FIG. 41 is a flow diagram illustrating an example method for validatinga data set.

FIG. 42 is a flow diagram illustrating an example method for groupingvalues of second modal frequencies into unique groups.

FIG. 43 is a flow diagram illustrating an example method for removingoutlier values of a first modal frequency and/or a second modalfrequency.

FIG. 44 is a flow diagram illustrating an example method for finding anoptimum group of values for a second modal frequency.

DESCRIPTION

References to items in the singular should be understood to includeitems in the plural, and vice versa, unless explicitly stated otherwiseor clear from the text. Grammatical conjunctions are intended to expressany and all disjunctive and conjunctive combinations of conjoinedclauses, sentences, words, and the like, unless otherwise stated orclear from the context. Recitation of ranges of values herein are notintended to be limiting, referring instead individually to any and allvalues falling within the range, unless otherwise indicated herein, andeach separate value within such a range is incorporated into thespecification as if it were individually recited herein. In thefollowing description, it is understood that terms such as “first,”“second,” “top,” “bottom,” “side,” “front,” “back,” and the like arewords of convenience and are not to be construed as limiting termsunless otherwise stated or clear from context.

As used herein, the terms “about,” “approximately,” “substantially,” orthe like, when accompanying a numerical value, are to be construed asindicating a deviation as would be appreciated by one of ordinary skillin the art to operate satisfactorily for an intended purpose. Ranges ofvalues and/or numeric values are provided herein as examples only, anddo not constitute a limitation on the scope of the describedembodiments. The use of any and all examples, or exemplary language(“e.g.,” “such as,” or “the like”) provided herein, is intended merelyto better illuminate the embodiments and does not pose a limitation onthe scope of the embodiments. The terms “e.g.,” and “for example” setoff lists of one or more non-limiting examples, instances, orillustrations. No language in the specification should be construed asindicating any unclaimed element as essential to the practice of theembodiments.

As used herein, the term “and/or” means any one or more of the items inthe list joined by “and/or”. As an example, “x and/or y” means anyelement of the three-element set {(x), (y), (x, y)}. In other words, “xand/or y” means “one or both of x and y”. As another example, “x, y,and/or z” means any element of the seven-element set {(x), (y), (z), (x,y), (x, z), (y, z), (x, y, z)}. In other words, “x, y, and/or z” means“one or more of x, y, and z.”

As used herein, the terms “exemplary” and “example” mean “serving as anexample, instance or illustration.” The embodiments described herein arenot limiting, but rather are exemplary only. It should be understoodthat the described embodiments are not necessarily to be construed aspreferred or advantageous over other embodiments. Moreover, the terms“embodiments of the invention,” “embodiments,” or “invention” do notrequire that all embodiments of the invention include the discussedfeature, advantage or mode of operation.

As used herein, the term “data” is a broad term and is to be given itsordinary and customary meaning to a person of ordinary skill in the art,and refers without limitation to any indicia, signals, marks, symbols,domains, symbol sets, representations, and any other physical form orforms representing information, whether permanent or temporary, whethervisible, audible, acoustic, electric, magnetic, electromagnetic, orotherwise manifested. The term “data” is used to represent predeterminedinformation in one physical form, encompassing any and allrepresentations of corresponding information in a different physicalform or forms.

As used herein, the terms “memory” and “memory device” are broad termsand are to be given their ordinary and customary meaning to a person ofordinary skill in the art, and refer without limitation to computerhardware or circuitry to store information. Memory or memory device canbe any suitable type of computer memory or other electronic storagemeans including, for example, read-only memory (ROM), random accessmemory (RAM), dynamic RAM (DRAM), static RAM (SRAM), ferroelectric RAM(FRAM), cache memory, compact disc read-only memory (CDROM),electro-optical memory, magneto-optical memory, masked read-only memory(MROM), programmable read-only memory (PROM), erasable programmableread-only memory (EPROM), electrically-erasable programmable read-onlymemory (EEPROM), rewritable read-only memory, flash memory, or the like.Memory or memory device can be implemented as an internal storage mediumand/or as an external storage medium. For example, memory or memorydevice can include hard disk drives (HDDs), solid-state drives (SSDs),optical disk drives, plug-in modules, memory cards (e.g., xD, SD,miniSD, microSD, MMC, etc.), flash drives, thumb drives, jump drives,pen drives, USB drives, zip drives, a computer readable medium, or thelike.

As used herein, the term “processor” is a broad term and is to be givenits ordinary and customary meaning to a person of ordinary skill in theart, and refers without limitation to processing devices, apparatuses,programs, circuits, components, systems, and subsystems, whetherimplemented in hardware, tangibly embodied software, or both, andwhether or not it is programmable. The term “processor” includes, but isnot limited to, one or more computing devices, hardwired circuits,signal-modifying devices and systems, devices and machines forcontrolling systems, central processing units, microprocessors,microcontrollers, programmable devices and systems, field-programmablegate arrays (FPGAs), application-specific integrated circuits (ASICs),systems on a chip (SoC), systems comprising discrete elements and/orcircuits, state machines, virtual machines, data processors, processingfacilities, digital signal processing (DSP) processors, and combinationsof any of the foregoing. A processor can be coupled to, or integratedwith, memory or a memory device.

As used herein, the term “network” is a broad term and is to be givenits ordinary and customary meaning to a person of ordinary skill in theart, and refers without limitation to any communication networkincluding, for example, an extranet, intranet, inter-net, the Internet,local area network (LAN), wide area network (WAN), metropolitan areanetwork (MAN), wireless local area network (WLAN), ad hoc network,wireless ad hoc network (WANET), mobile ad hoc network (MANET), or thelike.

FIG. 4 is a schematic diagram illustrating an example setup of a system400 for estimating tension in post-tensioned rods. Although FIG. 4illustrates post-tensioned rods as anchor rods 410 securing structure430 to concrete foundation 420, this is only for convenience toillustrate the principles of the invention. Indeed, the inventivesystems, methods, and apparatuses are not limited to anchor rods thatsupport a structure to concrete and can be applied to any post-tensionedrods used for structural support or strength.

As illustrated in FIG. 4 , anchor rod 410 includes a portion undertension that is below the concrete foundation 420 (not shown) andun-tensioned portion, cantilever 412, that extends above concrete 420and protrudes through anchor plate 404 and structure flange 432. In thecase of anchor rods that secure the base of a wind turbine tower toconcrete, cantilevers 412 typically fall within the range of about 5 to10 inches long. These lengths are provided for context only and do notlimit the invention. Indeed, the inventive systems, methods, andapparatuses are not constrained by any particular length of cantilevers.As further illustrated in FIG. 4 , nut 414 on cantilever 412 istightened to create a clamping force that helps secure structure 430 toconcrete foundation 420.

Sensors

The system 400 can include a sensor 440 that is detachably coupled tocantilever 412 at a first point, for example, near the top of cantilever412. Sensor 440 can be any type of sensor or transducer capable of orsuitable for capturing and/or providing data indicative of a vibrationalresponse of anchor rod 410. In some embodiments, sensor 440 can be anaccelerometer that outputs data proportional to acceleration associatedwith a vibrational response of anchor rod 410. For example, sensor 440can be a capacitive micro-electro-mechanical systems (MEMS)accelerometer, a piezoresistive accelerometer, a piezoelectricaccelerometer, or the like. In other embodiments, sensor 440 can be avelocity sensor that outputs data proportional to velocity associatedwith a vibrational response of anchor rod 410. For example, sensor 440can be a moving coil velocity sensor, a piezoelectric velocity sensor,or the like. In still other embodiments, sensor 440 can be adisplacement sensor that outputs data proportional to positionaldisplacement associated with a vibrational response of anchor rod 410.For example, sensor 440 can be a capacitive displacement sensor, aneddy-current displacement sensor, or the like.

As will be appreciated by those of ordinary skill in the art, dataoutput from sensor 440 can be processed, transformed, or the like. Forexample, displacement data output from a displacement sensor can bedifferentiated to provide velocity data, and differentiated a secondtime to provide acceleration data. Velocity data output from a velocitysensor can be differentiated to provide acceleration data. Similarly,acceleration data output from an accelerometer can be integrated toprovide velocity data, and integrated a second time to providedisplacement data. Velocity data output from a velocity sensor can beintegrated to provide displacement data. Further, although system 400illustrates only one sensor 440, additional sensors can be used. Forexample, two or more sensors 440 can be detachably coupled to cantilever412 at first and second points. The two or more sensors 440 can compriseany combination of accelerometers, velocity sensors, displacementsensors, or the like.

The use of more than one sensor 440 can be beneficial for severalreasons. For one, more than one sensor can be used to sense transversemotion of the cantilever in radially-different directions. Further, dataoutput from the sensors can be compared, averaged, etc. For example, ifdata from one sensor is insufficient for data analysis (e.g., the datais clipped, the data is too low in amplitude, etc.), data from theanother sensor may be sufficient. Thus, the use of multiple sensors canprovide redundancy, can increase efficiency, and can increase accuracy.The inventive systems, methods, and apparatuses are therefore notlimited to any particular type of sensor 440, nor to any particularnumber of sensors.

Orienting a Sensor

In the system 400, sensor 440 can be detachably coupled to cantilever412 using, for example, magnet 442. In other embodiments, other means ofdetachably coupling sensor 440 to cantilever 412 can be used including,for example, adhesives such as tape or glue, or wax. Sensor 440 can bedetachably coupled to cantilever 412 at a first point. The first pointcan be anywhere on cantilever 412 including, for example, on the side orthe top of cantilever 412, and near the top, near the middle, or nearthe bottom of cantilever 412. Ideally, sensor 440 will be coupled tocantilevers of post-tensioned rods at approximately the same locationeach time a vibrational response is initiated. In embodiments in whichthe first point is on the side of cantilever 412, the distance from thetop of cantilever 412 can be measured using any standard means, such asa tape measure or a ruler. However, to ensure consistent and preciseplacement of sensor 440 on cantilever 412, an orienting apparatus 500can be used.

FIG. 5 is right-side perspective view of an orienting apparatus 500. Asillustrated, orienting apparatus 500 can comprise an elongate structureand can include a first open channel 510 having a first sidewall 512.The first sidewall 512 can have a substantially half cylinder shapealong the length of the first open channel 510. The first open channel510 can have a first longitudinal axis 514. Orienting apparatus 500 caninclude a second open channel 520 having a second sidewall 522. Thesecond sidewall 522 can have a substantially half cylinder shape alongthe height of the second open channel 520. The second open channel 520can have a second axis 524 along its height. As illustrated in FIG. 5 ,the first axis 514 can be substantially perpendicular to the second axis524. As further illustrated, the first open channel 510 and second openchannel 520 are contiguous. Orienting apparatus 500 can further includea stopper wall 530 having an inner surface 532. Inner surface 532 can bedisposed internal to the top of the second open channel 520. Asillustrated in FIG. 5 , the inner surface 532 of stopper wall 530 can besubstantially perpendicular to the second axis 524.

FIG. 6 is a top perspective view of orienting apparatus 500. As furtherillustrated in FIG. 6 and explained above, the first open channel 510and the second open channel 520 have a contiguous boundary 534. Theboundary 534 can be located a minimum distance L from inner surface 532,which can be any value greater than 0. The distance L will dictate thedistance that sensor 440 is located from the top of anchor rod 410 whenorienting apparatus 500 is used to detachably couple sensor 440 toanchor rod 410. Thus, the distance L can be 0.1 inches, 0.25 inches, 0.5inches, 1 inch, 3 inches, 5 inches, etc., including any lesser, greater,or intermediate value. Preferably, the distance L is about 0.5 inches.As further illustrated in FIG. 6 , when second sidewall 522 has asubstantially half circular cylinder shape, second sidewall 522 can havea radius R, which can be any value greater than 0 that is larger thanthe radius of anchor rod 410. That is, as explained more fully below,orienting apparatus 500 can be used by disposing anchor rod 410 withinsecond open channel 520 to detachably couple sensor 440 to anchor rod410. Thus, second open channel 520 should be large enough to accommodateanchor rod 410. For example, radius R can be about 0.1 inches, 0.25inches, 0.5 inches, 1 inch, etc., including any lesser, greater, orintermediate value. Preferably, radius R is about 0.75 inches.

A preferred manner in which orienting apparatus 500 can be used todetachably couple sensor 440 to anchor rod 410 is now explained.Referring to FIG. 7 , sensor 440 can be attached to magnet 442 tofacilitate detachably coupling sensor 440 to anchor rod 410. Sensor 440and magnet 442 can be positioned inside the first open channel 510 oforienting apparatus 500 such that at least magnet 442 contacts the firstsidewall 512. Magnet 442 is preferably positioned inside first openchannel 510 so that a front part of magnet 442 is approximately flushwith second sidewall 522.

Referring now to FIG. 8 , an operator grasps orienting apparatus 500with the first open channel 510 and second open channel 520 facing down.While holding orienting apparatus 500, magnet 442, and sensor 440firmly, the operator places the second open channel 520 over cantilever412 until the top of cantilever 412 is in contact with inner surface 532of stopper wall 530 and magnet 442 is in contact with cantilever 412.After the operator removes orienting apparatus 500, which is illustratedin FIG. 9 , sensor 440 remains detachably coupled to cantilever 412 viamagnet 442.

Orienting apparatus 500 can be any shape and size that enables onoperator to consistently and precisely detachably couple sensor 440 toanchor rod 410. For example, the first open channel 510 of orientingapparatus 500 can be contoured to closely match the shape of thecomponents to be placed therein. This is illustrated in FIGS. 10-16 .

FIG. 10 is a front elevation view of an orienting apparatus 500 having acontoured first open channel 510. As illustrated, first open channel 510can have a first cavity 515 having a contour configured to match thedimensions of magnet 442, a second cavity 516 having a contourconfigured to match the dimensions of a fastening nut that couplesmagnet 442 to sensor 440, and a third cavity 517 having a contourconfigured to match the dimensions of sensor 440. In embodiments inwhich a transmission line is used to communicate data from sensor 440(as opposed to other means, such as wirelessly), first open channel 510can further include a fourth cavity 518 having a contour configured tomatch the dimensions of transmission line 452 and wings 519 configuredto hold transmission line 452. Wings 519 can help stabilize magnet 442,sensor 440, and transmission line 452 while an operator detachablycouples sensor 440 to cantilever 412. Wings 519 are best illustrated inFIGS. 14-16 .

Exciting a Post-Tensioned Rod

Embodiments disclosed herein can be used to estimate tension inpost-tensioned rods, for example, by modeling tension as a function of adifference in frequency between a first and a second modal frequency fora subset of rods, then using the model to estimate tension in otherrods. That is, a set of post-tensioned rods in situ can be used togenerate training data, which training data can be used to create amodel, which model can be used to estimate tension in a targetpost-tensioned rod. For both creating a model and to estimate tension ina post-tensioned rod, data associated with vibrational responses incantilevers of the post-tensioned rods is obtained. This data can bereceived from a sensor 440 detachably coupled to a post-tensioned rod410. A vibrational response can be initiated by imparting atransversely-directed impact on a cantilever of the post-tensioned rod.In some embodiments, the impact can be imparted manually, such as with ahammer or other striking tool. In other embodiments, the impact can beimparted with an automated impacting device. An automated impactingdevice can help provide a consistent level of force with each impact.Additionally, it can provide a means for accurately measuring andrecording the force of each impact, which can provide additional datapoints. An automated impacting device can also enable sweeping through aspectrum of different levels of force for each impact.

FIGS. 17 and 18 illustrate an example location on cantilever 412 atwhich anchor rod 410 may be impacted when a sensor 440 is detachablycoupled near the top of cantilever 412. FIG. 17 is a side elevation viewof cantilever 412 and nut 414. As illustrated, sensor 440 can bedetachably coupled at a first point near the top of cantilever 412 withmagnet 442. Cantilever 412 can be impacted at a second point 416. Asbetter illustrated in FIG. 18 , which is a front elevation view ofcantilever 412 and nut 414, second point 416 can be substantially inline with the first point at which sensor 440 is detachably coupled.That is, sensor 440 and second point 416 can generally lie on alongitudinal axis 415. Other locations on cantilever 412 may also beimpacted. However, it is believed that as the second point rotatesaround cantilever 412 and away from axis 415, the strength of avibrational response measured by sensor 440 may begin to diminish,potentially making it more difficult to receive data. Thus, nearly anypoint of cantilever 412 may be impacted, and it is believed that thestrongest vibrational response can be measured when second point 416 islocated along axis 415.

Receiver/External System

Data from sensor 440 can be transmitted to a receiver 450. For example,FIG. 19 is a simplified block diagram illustrating a sensor 440 incommunication with a receiver 450 according to some embodiments. Theoutput of sensor 440 can include analog signals, digital signals,pulse-width modulated (PWM) signals, and other types of signals. Datagenerated by sensor 440 (i.e., sensor data) associated with avibrational response can relate to time, voltage, acceleration,velocity, displacement, and other information. Sensor data can betransmitted from sensor 440 to receiver 450 via a wired or wirelessconnection 452. For example, in some embodiments, sensor data can betransmitted to receiver 450 via a coaxial transmission line (e.g., asillustrated in FIG. 4 ). Other types of wired connections may also beused as will be apparent to those of skill in the art. In otherembodiments, sensor data can be transmitted from sensor 440 to receiver450 via a suitable wireless technology such as, for example, a radiofrequency (RF) technology, near field communication (NFC), Bluetooth,Bluetooth Low Energy, IEEE 802.11x (i.e., Wi-Fi), Zigbee, Z-Wave,Infrared (IR), cellular, and other types of wireless technologies aswill be apparent to those of skill in the art. Although only one sensoris illustrated in FIG. 19 , it should be appreciated that any number ofsensors and/or types of sensors may be used. In the case of multiplesensors in communication with receiver 450, communication media 452 cancomprise a combination of both wired and/or wireless connections.

In some embodiments, such as that illustrated in FIG. 20 , receiver 450can be in communication with an external system 460. In someembodiments, external system 460 can comprise a computing device such asa tablet, smartphone, laptop computer, desktop computer, or the like.For example, receiver 450 can be a data acquisition device (DAQ) andexternal system 460 can be a computer. In some embodiments, externalsystem 460 can be a network, such as a private network, the Internet, orthe like. It should be noted that external system 460 need not be asingle system. Rather, external system 460 can comprise a combination ofcomputing devices, networks, servers, the Internet, or the like.Communication medium 462 can comprise a wired or wireless connection.For example, in some embodiments, communication medium 462 can be awired connection, such as a coaxial transmission line, USB cable,Ethernet cable, and other types of wired connections as will be apparentto those of skill in the art. In other embodiments, communication medium462 can be a suitable wireless technology such as, for example, a radiofrequency (RF) technology, near field communication (NFC), Bluetooth,Bluetooth Low Energy, IEEE 802.11x (i.e., Wi-Fi), Zigbee, Z-Wave,Infrared (IR), cellular, and other types of wireless technologies aswill be apparent to those of skill in the art. In the case of externalsystem 460 comprising multiple systems or devices, communication media462 can comprise a combination of both wired and/or wirelessconnections.

Receiver 450 can include hardware, firmware, and/or software thatgenerally enables a user to interact with the system, to receive datafrom sensor 440, to process the data, to analyze the data, to store thedata, and/or to transmit the data to external system 460. FIG. 21 is ablock diagram illustrating an example receiver 450 according to someembodiments. The receiver 450, which is communicatively coupled tosensor 440 via communication medium 452, can receive sensor data fromsensor 440 via an input/output (I/O) module 451. The I/O module 451 cansend the data to processor module 452.

Processor module 452 can be coupled to one or memory devices 453. Theone or more memory devices 453 can store data, such as data receivedfrom sensor 440, data received from a user, and data received from anexternal system 460. The one or more memory devices 453 can also storesoftware 454 (i.e., computer-executable instructions). Processor module452 can process data, wherein the processing can include, for example,amplifying, converting from analog to digital or digital to analog,conditioning, filtering, and/or transforming the data. Processor module452 can also serve as a central control unit of receiver 450. Forexample, software 454 can comprise operating system software, firmware,and other system software for controlling receiver 450 and itscomponents. Software 454 can further include data processing software,application software, or the like, as discussed in more detail below.

Receiver 450 can include a user interface 470 that comprises input andoutput components configured to allow a user to interact with receiver450. For example, user interface 470 can include a keyboard 471, mouse472, trackpad 473, touch-sensitive screen 474, one or more buttons 475,display 476, speaker 477, one or more LED indicators 478, and microphone479. Processor module 452 can control user interface 470 and itscomponents. For example, processor module 452 can receive data andcommands from input components through I/O module 451 and provide dataand commands to output components through I/O module 451. Processormodule 452 can execute software 454 stored in the one or more memorydevices 453 to cause a graphical user interface (GUI) to be displayed ondisplay 476. The GUI can provide the user with an intuitive anduser-friendly means for interacting with the system, including toprovide output to the user such as prompts, messages, notifications,warnings, alarms, or the like.

The components of the user interface 470 include controls to allow auser to interact with the receiver 450. For example, the keyboard 471,mouse 472, and trackpad 473 can allow input from the user. Thetouch-sensitive screen 474 can enable a user to interact with the GUI,for example, by inputting information, making selections, or the like.The one or more buttons 475 can provide for quick and easy selection ofoptions or modes, such as by toggling functions on/off. The display 476can be any type of display, such as an LCD, LED, OLED, or the like. Thedisplay 476 can provide the user with visual output. The speaker 477 canprovide the user with audible output, such as by alerting the user ofnotifications, warnings, alarms, or the like. The one or more LEDindicators 478 can provide the user with visual indications. Forexample, one LED indication might represent whether there is sufficientbattery power, or whether the receiver is receiving power from anexternal source. Another LED indication might inform the user whetherthe receiver 450 is in an active state and measuring data received fromsensor 440. The microphone 479 can provide a user with the capability tocontrol receiver 450 by voice. Although not illustrated, the userinterface 470 can include other components, such as a vibrating moduleto provide a user with tactile signals or alerts, a backlight tofacilitate viewing the display in low light conditions, or the like.

As further illustrated in FIG. 21 , receiver 450 can includecommunication module 455, which can comprise components, such astransceivers, drivers, antennas, and the like, to enable communicationwith various types of devices and systems. For example, communicationmodule 455 can include Ethernet ports, USB ports, and ports forcommunicating over RS-232, RS-422, RS-485, and other protocols.Communication module 455 can further include antennas and othercomponents typically used for wireless communication, such analogfrontend circuitry, A/D converters, amplifiers, filters, and the like.Communication module 455 can enable communication with an externalsystem 460. For example, an external system 460 may send commands ordata to, or receive commands or data from, receiver 450. Communicationmodule 455 may also enable receiver 450 to receive software updates.Thus, communication module 455 is a two-way communication module thatenables receiver 450 to communication with an external system 460.

As further illustrated in FIG. 21 , receiver 450 can include a powersupply 456, which can include rechargeable or disposable batteries.Power supply 456 may also include circuitry to receive power from anexternal source and to supply the necessary power to receiver 450, suchas through an AC adapter. In some embodiments, the external source canbe a computer that supplies power to receiver 450 over a USB cable.

Receiver 450 can support various other functions. For example, in someembodiments, receiver 450 can include the ability to record and playbackdata events received from sensor 440, while also permitting forreal-time display of the events. In some embodiments, receiver 450 caninclude the ability to tag events as they occur. For example, receiver450 can include one or more buttons 475 that enables a user to insert amarker onto data in real-time. In some embodiments, receiver 450 canpermit remote control and monitoring. For example, receiver 450 can becommunicatively coupled to an external system 460 to enable the externalsystem 460 to view data events in real time and to control receiver 450.

It should be noted that FIG. 21 is a functional block diagram and not astrict architectural diagram. Thus, FIG. 21 generally illustrates thefunction of components in receiver 450, some of which may be combinedand some of which may be separated. For example, some or all of thefunctionality of the I/O module 451 might be combined with some or allof the functionality of the communication module 455 and vice versa. Asanother example, communication module 455 may comprise severalindividual modules, some of which may communicate with sensor 440 via awired or wireless connection, while others may communicate with externalsystem 460 via a wired or wireless connection. As yet another example,processor module 452 may comprise several components, such as discreteprocessing elements for amplifying, converting, conditioning, filtering,and transforming data, and a microprocessor or microcontroller forcontrolling receiver 450 (in addition to performing other functions,such as further processing data). Further, the functional blocksillustrated in FIG. 21 are communicatively coupled in an appropriatemanner as would be appreciated by one of ordinary skill in the art. Forexample, the components can be communicatively coupled with a bus. Thus,commands, data, and other information received from the I/O module 451and communication module 455 would be transmitted to processor module452 for processing, storing, and or other action. Similarly, processor452 would transmit commands, data, and other information to I/O module451 and communication module 452, as appropriate, to be furthercommunicated to other components, such as sensor 440, external system460, and user interface 470 and its components.

Operation of the Inventive Systems

The operation of the systems to estimate tension in post-tensioned rodsare now explained. For convenience, reference will be made to thesystems illustrated in the figures. Generally, the tension in apost-tensioned rod in situ (i.e., a “target” post-tensioned rod) can beestimated by first creating a regression model using training data, thenusing the model to predict the tension in the target post-tensioned rod.The training data can be generated from a plurality of otherpost-tensioned rods. The plurality can comprise any number ofpost-tensioned rods. It has been found that, in the case ofpost-tensioned rods used to support structural steel to concrete, aplurality comprising 12 post-tensioned rods may suffice. As explained inmore detail below, the regression model will be based on at least adifference in frequency between first and second modal frequencies andcantilever lengths. Ideally, the post-tensioned rods selected for theplurality will have cantilever lengths that can be grouped evenly into anumber of groupings. For example, if 12 post-tensioned rods are selectedfor the plurality and have cantilever lengths that can be grouped intoone of four groupings of length, the plurality will comprise threepost-tensioned rods in each cantilever grouping that can be used togenerate the training data. Nevertheless, other configurations forcantilever groupings are possible as explained in more detail below.

Generating the training data. The training data can be generated byselecting one of the post-tensioned rods 410 in the plurality andsetting the rod to a known level of tension, for example, using ahydraulic jack with a tension gauge. The goal of the training data is tocorrelate different levels of tension with a difference in frequencybetween first and second modal frequencies and cantilever lengths.Therefore, a range of tension levels is preferably used to generate thetraining data, which may include levels of tension both above and belowthe specified design tension for the particular post-tensioned rodsbeing examined. For example, where the specified design tension is 320kN, it may be desirable to set the tension in each post-tensioned rodfrom 90 kN to 450 kN in 40-kN increments.

Once the first level of tension is set in the post-tensioned rod 410,the length of the cantilever of the rod can be measured and recorded.The cantilever length will typically vary based on the tension in therod. A sensor 440, such as an accelerometer, can be detachably coupledto the cantilever 412 of the post-tensioned rod 410 and communicativelycoupled to a receiver 450, such as the receiver 450 of FIG. 21 . Usingan impact device, the cantilever 412 can be impacted to initiate avibrational response, which can be measured by the accelerometer. Theaccelerometer, in turn, can transmit data associated with thevibrational response to the receiver 450. It is possible that the dataassociated with the vibrational response is insufficient for determininga first and/or a second modal frequency. For example, if the impact tocantilever 412 is too great, data received from the accelerometer mightbe clipped. If the impact to cantilever 412 is too soft, data receivedfrom the accelerometer might not have sufficient amplitude. In bothinstances, it may be necessary or desirable to impact cantilever 412again to generate another vibrational response.

In practice, it is common for a field person to rely on experience todetermine whether data from a vibrational response is clipped, too lowin amplitude, or contains other apparent anomalies. However, the datamay contain noise or other anomalies that are not readily apparent tothe field person, but which will make it difficult or impossible toidentify modal frequencies from the data. To address these concerns andto increase efficiency in generating the training data, receiver 450 cancomprise software in the one or more memory devices that, when executedby the processor, cause the processor to analyze the data in real-timeto determine whether it is sufficient to identify first and second modalfrequencies, and ultimately, to identify the modal frequencies and adifference therebetween.

For example, the software can first analyze the sufficiency of the datato either validate that the impact was sufficient or to prompt the fieldperson to impact the cantilever again to generate another vibrationalresponse. If the impact was not sufficient, the software can providefeedback to the field person, such as a notification or message onreceiver 450 that explains why the impact failed validation and what thefield person can do to correct it. If the software validates the impact,it can analyze the data to identify a first and second modal frequency,and a difference in frequency between the modal frequencies. Thesoftware can store this data and instruct the field person that the dataanalysis for that measurement was successful. Example algorithms forvalidating the impact made to the cantilever, for determining first andsecond modal frequencies, for determining a frequency difference betweenthe modal frequencies, and other data analysis are provided below.

It may be desirable to measure the vibrational response of thepost-tensioned rod 410 several times at the same level of tensionwithout readjusting the tension. For example, the vibrational responseof a particular rod can be measured 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ormore times. It may also be desirable to measure the vibrational responseof the post-tensioned rod 410 several times at the same approximatelevel of tension, but by resetting the tension. For example, where thetension in the rod was set to approximately 90 kN, the actual tensionmight have been 89.95 kN. Thus, several measurements can be made at89.95 kN as just explained, then the tension in the rod can be reset toapproximately 90 kN again. This time, however, the actual tension mightbe 90.03 kN. Several measurements can then be made at 90.03 kN as justexplained. This iterative process can be repeated any number of times.In some embodiments, the vibrational response is measured at least 8times for each level of tension, and the approximate level of tension isreadjusted at least 5 times, resulting in a data set comprising 40measurements for an approximate level of tension. By increasing the sizeof the data set, the effects of poor, noisy, anomalous, or otherwiseaberrant readings can be diminished.

Furthermore, it may also be desirable to determine the actual tension inthe rod after all measurements are made for a specific level of tension,but before the tension in the rod is reset to the same approximate levelof tension. The tension can be determined, for example, using thelift-off method. It may be desirable to determine the actual tension inthe rod even though it was set to a known level of tension because therod may release or give slightly after the tension was set, therebyresulting in a determined tension that differs slightly from the tensionthat was set.

Once all the necessary or desirable data has been collected and/orstored for the first-selected rod in the plurality of post-tensionedrods, the measurements outlined above can be repeated for each of theremaining rods in the plurality of post-tensioned rods.

In some embodiments, data collected during the measurements can beautomatically and/or manually stored in one or more memory devices, suchas memory 453 of receiver 450, as well as one or more external memorydevices connected to receiver 450. For example, software executing onthe receiver 450 can automatically store the collected data. As anotherexample, software on the receiver 450 can provide a GUI that enables theuser to enter data manually. For example, the GUI can provide variousfields for the user to enter measurements, such as tension levels set inthe post-tensioned rods, tension levels measured in the post-tensionedrods, cantilever lengths, and the like. Other data can also be stored inreceiver 450, whether entered manually or collected automatically, suchas the date and time when each measurement was made, GPS coordinates,weather conditions, thermal conditions of the post-tensioned rods,information about the user of the system, information about theequipment used to conduct the measurements, and the like. In otherembodiments, some or all of the data mentioned above can be stored in anexternal system 460 instead of, or in addition to, being stored inreceiver 450. For example, in some embodiments, receiver 450 stores datareceived from sensor 440 while the remaining data is stored in externalsystem 460. Thus, it is contemplated that the inventive systemsdisclosed herein can comprise a distributed system in which receiver 450and external system 460 work in concert to collect, process, store, andtransmit data related to the measurements and other parameters.

Modeling the training data. The training data can be analyzed to provideone or more models that correlates tension with a difference betweenfirst and second modal frequencies and cantilever lengths. The modelscan be used to estimate tension in other post-tensioned rods that werenot used to create the training data. It should be noted, however, thatnothing precludes using the models to also estimate tension in thepost-tensioned rods used to create the models. However, since thesepost-tensioned rods would have been set to various levels of tension tocreate the training data, it is presumed that the tension in these rodsis already known.

The data can be modeled by finding the frequency difference betweenfirst and second modal frequencies for each level of tension set whilecreating the training data and by grouping the cantilever lengths intoone or more groups. To determine the frequency difference between firstand second modal frequencies, the training data can be analyzed todetermine a value for the first modal frequency and a value for thesecond modal frequency that corresponds to each impact that was made,and thus, each vibrational response that was measured. The values forthe first and second modal frequencies can be found in numerous ways.One way is to convert temporal data received from the sensor, such as anaccelerometer, from the time domain to the frequency domain, then toidentify the first and second modal frequencies from the frequencydomain representation.

FIG. 22 illustrates an example of temporal data associated with avibrational response received from an accelerometer. The exampleillustrated in FIG. 22 is representative of training data that might beassociated with one impact to one post-tensioned rod at one level oftension. As illustrated in FIG. 22 , the x-axis corresponds to time andthe y-axis corresponds to acceleration data that has been normalized tocreate a unity peak amplitude. The temporal data illustrated in FIG. 22can be transformed to the frequency domain to obtain a frequencyresponse corresponding to the impact to the post-tensioned rod. Thetemporal data can be transformed using, for example, a Fourier Transformand in particular, a Fast Fourier Transform (FFT). An example frequencyresponse is illustrated in FIG. 23 . As illustrated, the first modalfrequency is identified as 2302 and the second modal frequency isidentified as 2304. Other methods to determine the value of the firstand second modal frequencies can be used. For example, the training datacan be analyzed with software that can determine the modal frequencies.Additionally, the algorithms discussed in more detail below can be used.

Once the values for the first and second modal frequencies aredetermined from the training data, the values for each can be averaged.The average first modal frequency can then be subtracted from theaverage second modal frequency to determine a frequency differencebetween the average first and second modal frequencies for each tensionlevel. An alternative approach that will produce the same results is tosubtract the first modal frequency from the second modal frequency foreach impact that was made, then to average the differences found foreach impact. It should be noted that, if only a single measurement wasmade on a particular post-tensioned rod for a given level of tension (oronly one measurement produced usable data to identify modalfrequencies), the average frequency difference will be the frequencydifference corresponding to that single measurement.

The lengths of the cantilevers measured at each tension level can begrouped into one or more groups. For example, where cantilevers of thepost-tensioned rods ranged from 5.5 to 7.5 inches long, the lengths ofthe cantilevers can be grouped, for example, into four equal groups,each spanning 0.5 inches. In this regard, group one could containcantilevers ranging between 5.5 to 6.0 inches long; group two from 6.0to 6.5 inches long; group three from 6.5 to 7.0 inches long; and groupfour from 7.0 to 7.5 inches long. These groupings are merely an exampleconfiguration. The cantilever lengths can be group in myriad other ways.For example, the cantilever lengths can be grouped into 1, 2, 3, 4, 5,6, 7, 8, 9, 10, and any greater number of groups. The groupings need notspan an equal distance. For example, a first group can span 0.25 inches,a second group can span 0.5 inches, and a third group can span 1.5inches. Thus, a group can span any size. The groupings also need notcontain an equal number of cantilevers. Thus, the cantilevers may begrouped in any number of ways and the inventive systems, methods, andapparatuses are not limited to any specific grouping configuration.

Regression analysis can be performed on the frequency differences andtension levels for each cantilever grouping. The tension levels used inthe analysis, and therefore associated with the frequency responses(i.e., frequency differences), can be the level of tension that was setin each post-tensioned rod while creating the training data, the levelof tension that was measured before resetting tension levels duringtraining, or an average of the two levels of tension. Once performed,the regression analysis can provide regression equations and/orregression plots that correlate the various levels of tension from thetraining data with frequency differences for each grouping.

FIG. 24 illustrates example regression plots for four cantilevergroupings, where the data for each grouping is identified by a differentsymbol (i.e., circles, triangles, squares, and diamonds). As illustratedin FIG. 24 , frequency differences are plotted along the x-axis andtension levels are plotted along the y-axis. In this example, tensionlevels ranging from 90 kN to 450 kN were set in the plurality ofpost-tensioned rods in 40-kN increments. The regression analysis wasperformed for the four cantilever groupings, resulting in the fourregression curves shown. Curve 2402 corresponds to cantilever group 1;curve 2404 corresponds to cantilever group 2; curve 2406 corresponds tocantilever group 3; and curve 2408 corresponds to cantilever group 4.

Estimating tension. The regression analysis can be used to estimatetension in a target post-tensioned rod. To do so, the length of acantilever of the post-tensioned rod and a frequency difference betweenfirst and second modal frequencies can be found in a manner similar tothat explained above in connection with generating the training data.That is, the length of the cantilever 412 of the target post-tensionedrod 410 can be measured and/or recorded. A sensor 440, such as anaccelerometer, can be detachably coupled to the cantilever 412 andcommunicatively coupled to a receiver 450, such as receiver 450 of FIG.21 . The cantilever 412 can be transversely-impacted one or more timesto initiate vibrational responses. The accelerometer can transmit dataassociated with the vibrational responses to receiver 450. From thereceived data, values for the first modal frequency and values for thesecond modal frequency can be determined. If more than one impact wasmade, these values can be averaged. The average first modal frequencycan be subtracted from the average second modal frequency to provide anaverage frequency difference between the modal frequencies.

The average frequency difference between first and second modalfrequencies for the target post-tensioned rod can be used tonon-destructively estimate tension in the rod based on at least themodel. For example, suppose the cantilever length of the targetpost-tensioned rod falls within the second cantilever grouping of themodel illustrated in FIG. 24 (i.e., curve 2404). Suppose further thatthe frequency difference for the post-tensioned rod is determined to be1950 Hz. Using the example model illustrated in FIG. 24 , thepost-tensioned rod would have an estimated tension of about 330 kN.Notably, this level of tension was estimated merely by measuring thecantilever length and determining the frequency difference of first andsecond modal frequencies in the target post-tensioned rod. Thus, oncethe training data is used to create a model, the process of estimatingtension in other post-tensioned rods can be scaled rapidly. Indeed, thetension in all anchor rods at an entire wind farm, for example, can beestimated in a small fraction of the time than with current methods.

The model of FIG. 24 was used above to illustrate the principles of theinvention. In practice, tension would typically be estimated based onthe model using a software program. Software can add speed, precision,and efficiency over manually using graphs to identify estimated levelsof tension. Thus, an alternative way to estimate tension in a targetpost-tensioned rod is to enter the training data, along with the datafor the frequency difference and cantilever length of the targetpost-tensioned rod, into a software program that can analyze the dataand generate a regression model that best fits the data, as well as anestimate for the tension in the target post-tensioned rod based on themodel.

For example, once the training data and the data for the targetpost-tensioned rod are entered, the software program can analyze thedata to determine which type of regression model results in the lowestmean absolute error (MAE). Example regression models include a DecisionTree Regressor, Random Forest Regressor, Gradient Boosting Regressor,XGB Regressor, K-Neighbors Regressor, Extra Trees Regressor, StackingRegressor, Kernel Ridge, Ridge, Linear SVR, Keras Regressor, Lasso, SGDRegressor, MLP Regressor, SVR, Linear Regression, and Dummy Regressor.Other regression models can be considered and/or used as will beapparent to those of skill in the art. Based on the regression modelselected, the training data, and the data associated with the targetpost-tensioned rod, the software program can provide an estimate for thetension in the target post-tensioned rod.

In addition to speed, precision, and efficiency, there are several otheradvantages of using the software program. For one, additional parameterscan be input into the program to expand the data set for regressionmodeling. For example, the thermal condition of the post-tensioned rod,the size of the post-tensioned rod, and the time that it takes thevibrational response to dampen to a certain threshold can be input intothe program. These additional parameters can help improve the accuracyof the estimations. Another benefit is that the program can identifywhen one parameter is a function of another parameter and therebyprovide insight into which parameters to consider when procuringtraining data. Still another benefit is that the regression analysis isnot dependent on any particular model, but rather will be based on themodel that produces the lowest MAE. A regression model for one set oftraining data may not be the best-fit model for another set of trainingdata.

Still another benefit of using software is that it can be loaded ontothe receiver, such as the receiver 450 illustrated in FIG. 21 . In thisregard, receiver 450 can be an all-in-one unit for modeling tension withtraining data and estimating tension in post-tensioned rods. Forexample, receiver 450 can be a computing device, such as a tablet, thatinterfaces with a sensor 440 and receives sensor data associated withvibrational responses of post-tensioned rods. Receiver 450 can processand analyze the data to model tension as a function of differences infrequency for first and second modal frequencies of the post-tensionedrods. Receiver 450 can further receive input from a user associated withthe length of cantilevers of the post-tensioned rods. Receiver 450 canthen analyze the data and provide an estimate for tension in a targetpost-tensioned rod based on at least the model. Receiver 450 can includeother functions, such as the ability to generate audit reports for aplurality of target post-tensioned rods, such as anchor rods used tosupport wind turbines at a wind farm.

In other embodiments, receiver 450 can be a data acquisition device(DAQ) configured to receive data from sensor 440, process the data,store the data, and optionally transmit the data to an external system460. For example, external system 460 can be a computing device thatcontains software for analyzing the data received from the DAQ 450.Alternatively, external system 460 can comprise a network. Data from DAQ450 can be transmitted to the network for offsite analysis. Otherconfigurations in which receiver 450 and/or external system 460 receivedata from sensor 440, process and analyze the data, and provideestimates for tension are possible and contemplated herein.

Distinguishing between models with signal damping. One potentialdifficulty that can arise when estimating tension in a targetpost-tensioned rod based on a model is that the frequency differencedetermined for the post-tensioned rod may correspond to two cantilevergroupings and thus, potentially two different levels of tension. Thispotential difficulty can be exacerbated if the cantilever length of thetarget post-tensioned rod is on the cusp of two cantilever groupings.For example, returning to FIG. 24 , a frequency difference of 1950 Hzcorresponds to about 330 kN for cantilever grouping 2 (i.e., curve 2404)as previously explained; however, it also corresponds to a tension ofabout 170 kN for cantilever grouping 3 (i.e., curve 2406). If thecantilever length of the target post-tensioned rod is on the cusp ofcantilever groups 2 and 3, it may be difficult to discern whether 330 kNor 170 kN is the more accurate estimate for tension in the targetpost-tensioned rod.

One approach to address this situation is to select the regression curvethat results in the least amount of estimated tension. Although thetension may be underestimated with this approach, it should promptfurther investigation to determine whether the tension complies with aspecified design tension for the rod, which is favored over thealternative—potentially overestimating tension and allowing anunder-tensioned rod to go unaddressed.

Another approach is to identify the correct model based on signaldamping. It is believed that the time it takes the vibrational responseto dampen in a post-tensioned rod can be correlated to the tension inthe rod. For example, where two post-tensioned rods have approximatelythe same cantilever lengths and are impacted with approximately the sameforce, the vibrational response should dissipate sooner in the rod at ahigher tension. Thus, if the frequency difference measured in the targetpost-tensioned rod corresponds to two regression models, signal dampingmay be used to resolve which model is more accurate. Preferably, forsignal damping to distinguish regression models, an automated impactingdevice should be used to impact the plurality of post-tensioned rods tocreate the training data as well as the target post-tensioned rod. Anautomated impacting device can help deliver a consistent level of forcefor each impact, thus correlating the signal damping with tension ineach of the post-tensioned rods.

Signal damping is based on decay time, which is the time that it takesthe vibrational response to dampen to a certain threshold. For example,the threshold can be about ten percent (10%) of the maximum amplitude ofthe received data. FIG. 25 is a graph diagram illustrating dataassociated with a vibrational response and a decay time that correspondsto a threshold of 10%. As illustrated, the amplitude of the receiveddata along the y-axis has been normalized. Thus, a threshold of 10%corresponds to an amplitude of 0.1, which is illustrated in FIG. 25 withline 2502. The decay time corresponding to 0.1 is approximately 22 μs,which is illustrated in FIG. 25 with line 2504. Where the targetpost-tensioned rod is impacted more than one time, the decay timescorresponding to each of the vibrational responses can be averaged tofind an average decay time.

The average decay time can be used to distinguish between regressionmodels. For example, if the average frequency difference for the targetpost-tensioned rod corresponds to only one tension level (and thus, onecantilever grouping), that tension level is the estimated tension in thetarget post-tensioned rod. If, instead, the average frequency differencefor the target post-tensioned rod corresponds to more than one tensionlevel (and thus, more than one cantilever grouping), the average decaytime can be analyzed to determine whether it is above or below a certainthreshold. For example, where the threshold is 20 μs and the averagedecay time is found to be 22 μs, the estimated tension in the targetpost-tensioned rod would be the lower level of tension in the model.That is because the vibrational response dampened at a slower rate thanthe threshold of 20 μs. If the average decay time had been less than the20 μs-threshold, the estimated tension in the target post-tensioned rodwould be the high level of tension in the model because the vibrationalresponse dampened at a faster rate.

EXAMPLE METHODS

Several testing protocols or methods provided by the inventions areprovided below. All or some portions of these methods may be implementedwith computer-executable instructions stored on one or more memorydevices that are executed by a processor.

FIG. 26 is a flow diagram illustrating an example method for estimatingtension in a target post tensioned rod. The method of FIG. 26 will bedescribed with reference to the figures. In other examples, additionalor alternative systems or components can be used to perform the methodof FIG. 26 .

Upon starting at step 2602, a plurality of post-tensioned rods can beselected at step 2604. At step 2606, tension for the plurality ofpost-tensioned rods can be modeled as a function of frequencydifferences between a first and a second modal frequency and cantileverlength of each rod. At step 2608, the length of a cantilever of thetarget post-tensioned rod can be measured. At step 2610, a first modalfrequency of the target post-tensioned rod can be determined. At step2612, a second modal frequency of the target post-tensioned rod can bedetermined. At step 2614, a frequency difference between the first modalfrequency and the second modal frequency for the target post-tensionedrod can be determined. At step 2616, tension in the targetpost-tensioned rod can be estimated based on at least the model. Themethod ends at step 2618.

FIG. 27 is a flow diagram illustrating an example method for modelingtension for a plurality of post-tensioned rods. The method can be used,for example, in connection with method 2600 of FIG. 26 . The method ofFIG. 27 will be described with reference to the figures. In otherexamples, additional or alternative systems or components can be used toperform the method of FIG. 27 .

Upon starting at step 2702, a rod within the plurality of post-tensionedrods can be selected at step 2704. At step 2706, a frequency response ofthe selected rod at the level of tension can be obtained. At step 2708,the length of a cantilever portion of the selected rod at the level oftension can be recorded. At step 2710, it can be determined whether moremeasures on the selected rod are needed or desired. For any of thereasons explained above, several measurements can be made on eachselected rod for each specified level of tension. If additionalmeasurements are to be made, at step 2712 the tension in the selectedrod can be adjusted if necessary. For example, multiple measurements canbe made at a specific level of tension set in the rod. The tension inthe rod can also be reset to the same approximate level of tension foradditional measurements, as explained above. Thus, tension can beadjusted, if necessary, at step 2712 and steps 2706 through 2710 can berepeated. If, at step 2710, it is determined that additionalmeasurements on the selected rod are not needed or desired, at step2714, it can be determined whether there are additional rods in theplurality for measurements. If there are additional rods, steps 2704through 2714 can be repeated. If, at step 2714, it is determined thatthere are no additional rods, at step 2716, frequency differencesbetween first and second modal frequencies at each of the one or morelevels of tension can be determined from the frequency responses foreach post-tensioned rod in the plurality. At step 2718, the cantileverlengths can be grouped into one or more groups. At step 2720, regressionanalysis can be performed for each group, wherein the regressionanalysis is based on at least the frequency differences and the levelsof tension. The method ends at step 2722.

FIG. 28 is a flow diagram illustrating an example method for obtaining afrequency response for one or more levels of tension. The method can beused, for example, in connection with method 2700 of FIG. 27 . Themethod of FIG. 28 will be described with reference to the figures. Inother examples, additional or alternative systems or components can beused to perform the method of FIG. 28 .

Upon starting at step 2802, tension in the post-tensioned rod can be setto a specified level at step 2804. At step 2806, a sensor can bedetachably coupled to the cantilever portion of the post-tensioned rod.At step 2808, a transversely-directed impact can be applied to thecantilever portion of the post-tensioned rod. At step 2810, temporaldata associated with a vibrational response can be received from thesensor. At step 2812, the temporal data can be transformed to thefrequency domain to obtain a frequency response. At step 2814, it can bedetermined whether more data is needed or desired for the specifiedlevel of tension. For any of the reasons explained above, severalmeasurements can be made on a post-tensioned rod at each level oftension set in the rod. If more data is needed or desired, steps 2808through 2814 can be repeated. If, at step 2814, it is determined thatmore data is not needed or desired, at step 2816, the level of tensionin the post-tensioned rod can be measured. At step 2818, a level oftension in the post-tensioned rod can be associated with the frequencyresponses. The level of tension associated can be the tension level set,the tension level measured, or a combination of both as explained above.At step 2820, it can be determined whether additional measurements areto be made on the post-tensioned rod (e.g., additional tension levels).If additional measurements are to be made, at step 2804, tension can beset in the rod to a specified level and steps 2806 through 2820 can berepeated. If, at step 2820, it is determined that additionalmeasurements are not needed, the method can end at step 2822.

FIG. 29 is a flow diagram illustrating an example method fordetermining, from frequency responses for each post-tensioned rod in aplurality, frequency differences between first and second modalfrequencies at each of one or more levels of tension. The method can beused, for example, in connection with method 2700 of FIG. 27 . Themethod of FIG. 29 will be described with reference to the figures. Inother examples, additional or alternative systems or components can beused to perform the method of FIG. 29 .

Upon starting at step 2902, the frequency responses for all levels oftension for the post-tensioned rod can be provided. At step 2904, thefrequency responses for a specified level of tension can be selected. Atstep 2906, a value for the first modal frequency from each frequencyresponse for the specified level of tension can be determined. At step2908, a value for the second modal frequency from each frequencyresponse for the specified level of tension can be determined. At step2910, an average of the values of the first modal frequency can bedetermined. At step 2912, an average of the values for the second modalfrequency can be determined. At step 2914, a frequency differencebetween the average first modal frequency and the average second modalfrequency can be determined. At step 2916, it can be determined whetherthere are frequency responses for additional levels of tension. If thereare additional frequency responses, at step 2904, the frequency responsefor another specified level of tension can be selected and steps 2906through 2916 can be repeated. If, at step 2916, it is determined thatthere are no additional frequency responses to consider, the method canend at step 2918.

FIG. 30 is a flow diagram illustrating an example method for determininga modal frequency (e.g., first, second, etc.) of a target post-tensionedrod. The method can be used, for example, in connection with method 2600of FIG. 26 . The method of FIG. 30 will be described with reference tothe figures. In other examples, additional or alternative systems orcomponents can be used to perform the method of FIG. 30 .

Upon starting at step 3002, a sensor can be detachably coupled to thecantilever portion of the target post-tensioned rod at step 3004. Atstep 3006, a transversely-directed impact can be applied to thecantilever portion of the target post-tensioned rod. At step 3008, dataassociated with a vibrational response can be received from the sensor.At step 3010, it can be determined whether additional data is needed ordesired. For any of the reasons explained above, several measurementscan be made on a post-tensioned rod. If additional data is needed ordesired, steps 3006 through 3010 can be repeated. If, at step 3010, itis determined that additional data is not needed or desired, at step3012, a value for the modal frequency of interest (e.g., first, second,etc.) can be determined for all of the impacts. At step 3014, a modalfrequency of interest for the target post-tensioned rod can bedetermined based on an average of the values for the modal frequency forall of the impacts. The method ends at step 3016.

FIG. 31 is a flow diagram illustrating an example method for determininga decay time for a target post-tensioned rod. The method can be used,for example, in connection with method 2600 of FIG. 26 . The method ofFIG. 31 will be described with reference to the figures. In otherexamples, additional or alternative systems or components can be used toperform the method of FIG. 31 .

Upon starting at step 3102, a sensor can be detachably coupled to acantilever portion of the post-tensioned rod at step 3104. At step 3106,a transversely-directed impact can be applied to the cantilever portionof the target post-tensioned rod. At step 3108, data associated with avibrational response can be received from the sensor. At step 3110, itcan be determined whether additional data is needed or desired. For anyof the reasons explained above, several measurements can be made on apost-tensioned rod. If additional data is needed or desired, steps 3106through 3110 can be repeated. If, at step 3110, it is determined thatadditional data is not needed, a decay time for each of the one or moreimpacts can be determined from the received data, wherein the decay timeis the time that it takes the vibrational response to dampen to athreshold. At step 3114, a decay time for the target post-tensioned rodcan be determined based on an average of the decay times for the one ormore impacts. The method ends at step 3116.

FIG. 32 is a flow diagram illustrating an example method for estimatingtension in a target post-tensioned rod. The method of FIG. 32 will bedescribed with reference to the figures. In other examples, additionalor alternative systems or components can be used to perform the methodof FIG. 32 .

Upon starting at step 3202, at step 3204, frequency differences betweenfirst and second modal frequencies for each rod in a plurality ofpost-tensioned rods can be determined, wherein the frequency differencesare determined for each rod at one or more levels of tension. At step3206, a frequency difference between first and second modal frequenciesfor the target post-tensioned rod can be determined. At step 3208,cantilever lengths of each rod in the plurality of post-tensioned rodscan be measured, wherein the cantilever lengths are measured for eachrod at one or more levels of tension. At step 3210, the cantileverlength of the target post-tensioned rod can be measured. At step 3212,regression analysis can be applied to estimate tension in the targetpost-tensioned rod, wherein the regression analysis is based on at leastthe frequency differences determined for the plurality of post-tensionedrods, the frequency difference for the target post-tensioned rod, themeasured cantilever lengths for the plurality of post-tensioned rods,and the measured cantilever length of the target post-tensioned rod. Themethod ends at step 3214.

EXAMPLE ALGORITHMS AND METHODS FOR ANALYZING DATA RECEIVED FROM A SENSOR

As explained above, software can be used to analyze the sufficiency ofdata received from a sensor, such as an accelerometer, to validate thatan impact was sufficient or to prompt the field person to impact thecantilever of a post-tensioned rod to generate another vibrationalresponse. The software can also analyze data received from a sensor todetermine first and second modal frequencies, determine a frequencydifference between modal frequencies, and the like. In some embodiments,the software can reside on receiver 450. In other embodiments, thesoftware can reside on external system 460. In still other embodiments,the software can reside on both receiver 450 and external system 460.For example, some of the steps of the following methods can be carriedout in software on receiver 450 while other steps can be carried out insoftware on external system 460. Some steps of the following methods maynot be carried out in software at all. Thus, the inventive methodsdescribed below are not limited by implementation.

FIG. 33 is a flow diagram illustrating an example method for determininga frequency difference between first and second modal frequencies of apost-tensioned rod. The determination is based on data received from asensor, such as an accelerometer, associated with a vibrational responseof a post-tensioned rod. The method of FIG. 33 can be applied, forexample, in connection with one or more measurements made on the samepost-tensioned rod. That is, the method can be repeated for multiplemeasurements on the same rod until enough valid impacts are made and afrequency difference can be determined. Additionally or alternatively,the method can be repeated for the same rod until it is performed amaximum number of times. The method of FIG. 33 can be applied whencreating training data to build a model and when determining a frequencydifference for a target post-tensioned rod, for example.

The method of FIG. 33 begins at step 3302 by receiving data associatedwith a vibrational response, such as from an accelerometer. At step3304, it can be determined whether the impact to the cantilever of thepost-tensioned rod is validated based on the received data. For example,the data can be analyzed to determine whether it is usable or suitablefor identifying a first modal frequency and/or a second modal frequency.If the received data is not validated at step 3304, the method of FIG.33 can indicate, at step 3306, that the impact failed validation and, atstep 3308, feedback can be provided regarding why the impact failedvalidation. At step 3340, the method of FIG. 33 can prompt the operatorperforming the measurements to impact the cantilever of thepost-tensioned rod again. The method can resume at step 3302 if anadditional impact is made.

If the received data is validated at step 3304, the received data can beanalyzed at step 3310 to determine a value for the second modalfrequency (F2). At step 3312, the method of FIG. 33 can indicate thatthe impact passed validation. At step 3314, a data set can be stored,for example, for later analysis. The data set can include, among otherthings, data received from the impact, the value for F2 determined atstep 3310, and other related data. The related data can include, amongother things, a value for the first modal frequency (F1) (e.g., whenfound during a previous step, such as steps 3304 or 3310) and confidencelevels related to F2. It will be appreciated by those of skill in theart that the related data is not limited thereto, but can include otherinformation such as the date and time related to a measurement, theidentity of the operator conducting the measurement, information aboutthe equipment used to conduct the measurement, weather conditions,thermal condition of the post-tensioned rod, and more.

At step 3316, it can be determined whether additional data is needed.Additional data may be needed for any of the reasons explained above. Ifadditional data is needed at step 3316, the method of FIG. 33 , at step3340, can prompt the operator performing the measurements to impact thecantilever of the post-tensioned rod again. The method can resume atstep 3302 if an additional impact is made.

If it is determined at step 3316 that additional data is not needed, itcan be determined at step 3318 whether a data set comprising the datastored at step 3314 for each impact can be validated. For example, thedata set can be analyzed to determine whether the stored data issufficient for determining a frequency difference between first andsecond modal frequencies (ΔF). The data may not be sufficient, forexample, where some or all of the values determined for the second modalfrequency vary significantly. By way of example only, suppose a data setcontains values for the second modal frequency of 2485 Hz, 2489.2 Hz,2491 Hz, 2491.7 Hz, and 2600 Hz. In this example, the first four valuesdiffer by no more than 7 Hz, whereas the value of 2600 Hz differs bymore than 100 Hz. Thus, the value of 2600 Hz may be disregarded, leavingonly four data points. If the minimum number of desired data points isfive, the example data set might not be validated and the method of FIG.33 , at step 3320, can indicate that the data set failed validation.

Where a data set fails validation, the method of FIG. 33 , at step 3322,can determine whether a maximum number of valid impacts to thecantilever has been received and, if so, indicate at step 3324 that thetesting should cease and end the method at step 3326. If the maximumnumber of valid impacts to the cantilever has not been received, themethod of FIG. 33 can, at step 3340, prompt the operator performing themeasurements to impact the cantilever of the post-tensioned rod again.The method can resume at step 3302 if an additional impact is made. Thedetermination at step 3322 regarding whether a maximum number of validimpacts has been received can be useful, for example, where an operatormakes several valid impacts to a cantilever (e.g., passing the conditionof step 3304), but the resulting data cannot be used to determine afrequency difference. Rather than the operator repeatedly striking acantilever and never reaching a determination of a frequency difference,a maximum amount of valid impacts can be set, for example, to sixteen.If the maximum number of valid impacts has been reached but theresulting data is not usable to find a frequency difference, theoperator can move on to another cantilever and restart the measurements.

If the data set is validated at step 3318 (e.g., ΔF can be determined),the method of FIG. 33 can proceed to step 3328 to determine a frequencydifference between the average values for the first and second modalfrequencies (ΔF_(MEAN)) and subsequently end at step 3330. It should benoted that, if the method of FIG. 33 is performed with only one valuefor the first and second modal frequencies, average values for eachfrequency will be the values found.

Impact validation. As discussed above in connection with step 3304 ofthe method of FIG. 33 , an impact made to a cantilever may or may not bevalid. An impact may not be valid where the resulting data is not usableor suitable for determining a first and/or second modal frequency. Tomake this determination, the resulting data can be analyzed in the timedomain and/or the frequency domain to determine whether it meets certaincriteria.

FIG. 34 is a flow diagram illustrating an example method for determiningwhether an impact made to a cantilever is valid. The method of FIG. 34begins at step 3402 with data being received from a sensor, such as anaccelerometer, resulting from impacting a cantilever of a post-tensionedrod. At step 3404, an initial confidence level corresponding to theimpact can be set. The confidence level can be adjusted as the receiveddata is analyzed. For example, confidence can be divided into threelevels, such as 1, 0.5, and 0, where 1 is the highest confidence and 0is the lowest confidence. The confidence level may provide insight aboutthe accuracy of the data and used in subsequent analyses. Thus, at step3404, the initial confidence level can be set to the highest level, suchas 1. After step 3404, the time domain (TD) waveform or the frequencydomain (FD) waveform can be analyzed. If the received data is in thetime domain, it may be more efficient to analyze the time domainwaveform first. If the received data is in the frequency domain, it maybe more efficient to analyze the frequency domain waveform first.However, the data can be analyzed in either domain first (presuming thedata will be analyzed in both domains), or it can be analyzed in onlyone of the domains. If the received data is in one domain and is to beanalyzed in the other domain, an appropriate mathematical transform canbe used, such as a Fourier Transform or an inverse Fourier Transform.For convenience, the following description begins with an explanation ofanalyzing the time domain representation of the received data (step3410).

At step 3412, the received data can be analyzed in the time domain todetermine a maximum amplitude of the received data. If the maximumamplitude exceeds a certain threshold, such as an operating range of thesensor, the condition at step 3412 is not satisfied. This is typicallyreferred to as clipping. Consequently, the impact fails validation (step3420) and the method is ended. If the maximum amplitude is below thethreshold, the condition at step 3412 is satisfied. The method canproceed to step 3414 to test another condition of the time domainwaveform, proceed to step 3450 and the impact can be consideredvalidated, or proceed to step 3430 to analyze the frequency domainwaveform (not shown by arrow).

At step 3414, the received data can be analyzed in the time domain todetermine whether noise is present in a first range of the receiveddata, such as before the primary waveform begins. This is referred to aspre-triggered noise and could be caused, for example, by the operatornot allowing enough time to pass between impacts and thus impacting therod while it is still vibrating from a previous impact. Pre-triggerednoise can also be caused by vibrating sources nearby, such as agenerator. Pre-triggered noise could be detected in several ways. Oneexample is to divide the first range into sections and, for eachsection, find the average amplitude and the standard deviation. Then,determine the standard deviation of all the section averages and theaverage of all the section standard deviations. If the ratio of thestandard deviation of all the section averages to the average of all thesection standard deviations is above a certain threshold, the conditionat step 3414 is not satisfied. Consequently, the impact fails validation(step 3420) and the method is ended. If the ratio of the standarddeviation of all the section averages to the average of all the sectionstandard deviations is below the threshold, the condition at step 3414is satisfied. The method can proceed to step 3416 to test anothercondition of the time domain waveform, proceed to step 3450 and theimpact can be considered validated, or proceed to step 3430 to analyzethe frequency domain waveform (not shown by arrow).

At step 3416, the received data can be analyzed in the time domain todetermine a minimum amplitude of the received data. If the minimumamplitude is below a certain threshold, such as two percent (2%) of themaximum allowable amplitude, the received data may not be usable todetermine first and/or second modal frequencies and the condition atstep 3416 is not satisfied. Consequently, the impact fails validation(step 3420) and the method is ended. If the minimum amplitude is abovethe threshold, the condition at step 3416 is satisfied. The method canproceed to step 3418 to test another condition of the time domainwaveform, proceed to step 3450 and the impact can be consideredvalidated, or proceed to step 3430 to analyze the frequency domainwaveform (not shown by arrow).

At step 3418, the received data can be analyzed in the time domain todetermine the rate of decay of the received data. If the time-domainwaveform does not decay at a consistent exponential rate until steadystate as expected, the received data may have post-triggered noise andtherefore may not be usable to determine first and/or second modalfrequencies. FIG. 35 illustrates an example waveform having a rate ofdecay that decreases exponentially until steady state. In contrast, FIG.36 illustrates an example waveform that does not decrease exponentiallyuntil steady state. For example, there is an abrupt change in theamplitude of the waveform at approximately 18 μs. Thus, the waveformillustrated in FIG. 36 might be an example of post-triggered noise.Other examples of waveforms that do not decrease exponentially untilsteady state are possible. If the amount of post-triggered noise exceedsa certain threshold, the condition at step 3418 is not satisfied.Consequently, the impact fails validation (step 3420) and the method isended. If post-triggered noise is present and is below the threshold,the condition at step 3418 is satisfied. The method can proceed to step3450 and the impact can be considered validated, or it can proceed tostep 3430 to analyze the frequency domain waveform (not shown by arrow).

The frequency domain waveform can be analyzed at step 3430, whetherbefore the time domain waveform is analyzed or after one or moreconditions of the time domain waveform have been analyzed.

At step 3432, the received data can be analyzed in the frequency domainto determine an amount of noise present in the frequency-domainwaveform. If the amount of noise exceeds a first threshold, the receiveddata may not be usable to determine first and/or second modalfrequencies. Noise in the frequency-domain waveform could be detected inseveral ways. One example is to determine whether the absolutedisplacement of amplitudes of the waveform for all frequencies within aspecified range, exclusive of displacements likely associated with F2,exceeds the first threshold. This can be determined, for example, byfinding the likely amplitude of F1, normalizing all frequencies in thefrequency-domain waveform to the F1 amplitude, specifying a range offrequencies where F2 is likely to be found, and summing the absolutevalue for all amplitude changes within that range. From the sum, theabsolute value for all amplitude changes likely associated with F2 canbe subtracted. If the result is above the first threshold, for example,1.5 times the amplitude of F1, the condition at step 3432 is notsatisfied. Consequently, the impact fails validation (step 3440) and themethod is ended. If the result is below the first threshold, thecondition at step 3432 is satisfied. Additionally, a second threshold,which is lower than the first threshold, can be set to adjust theconfidence level if it is exceeded. For example, although the amount ofnoise present in the frequency-domain waveform may have been less thanthe first threshold and therefore the condition at step 3432 issatisfied, the amount of noise may still be prevalent enough to callinto question the accuracy of the data. Thus, if the amount of noiseexceeds the second threshold, the confidence level can be adjusted from1 to 0.5 (or kept at 0.5 if previously adjusted). Because the conditionat step 3432 was satisfied, the method can proceed to step 3434 to testanother condition of the frequency domain waveform, proceed to step 3450and the impact can be considered validated, or proceed to step 3410 toanalyze the time domain waveform (not shown by arrow).

At step 3434, the received data can be analyzed to determine whethermultiples of a likely frequency value for F1 have amplitudes that maypotentially mask the value of F2, thereby rendering the received dataunusable to determine the second modal frequency. An example of thisphenomenon is illustrated in FIG. 37 . As shown, the frequency-domainwaveform contains periodic amplitudes at frequencies approximatelycorresponding to multiples of F1. Whether this phenomenon maypotentially mask the value of F2 can be determined in several ways. Oneexample is to find an FFT of the frequency-domain waveform (e.g., an FFTof an FFT). An example is illustrated in FIG. 38 , which is an FFT ofthe waveform illustrated in FIG. 37 . From the resulting waveform,determine an amplitude corresponding to the period of F1 (i.e., 1/F1).If that amplitude is greater than an amplitude of the closest localmaxima corresponding to a value less than 1/F1 or greater than anamplitude corresponding to twice the period of F1 (i.e., 2/F1), thecondition at step 3434 is not satisfied. Consequently, the impact failsvalidation (step 3440) and the method is ended. If the amplitude at 1/F1is less than both an amplitude of the closest local maxima correspondingto a value less than 1/F1 and the amplitude corresponding to 2/F1, thecondition at step 3434 is satisfied. The method can proceed to step 3436to test another condition of the frequency domain waveform, proceed tostep 3450 and the impact can be considered validated, or proceed to step3410 to analyze the time domain waveform (not shown by arrow).

At step 3436, the received data can be analyzed in the frequency domainto determine whether multiple local maxima may obscure the value of F2,thereby rendering the received data unusable to determine first and/orsecond modal frequencies. This can be determined, for example, byfinding the width of each local maxima corresponding to half of the peakamplitude of the maxima and determining whether the widths exceed acertain threshold. If at least three local maxima have both widths thatexceed the threshold and amplitudes that exceed half of the maximumpossible F2 amplitude, the condition at step 3436 is not satisfied.Consequently, the impact fails validation (step 3440) and the method isended. If the widths do not exceed the threshold, the condition at step3436 is satisfied. The method can proceed to step 3438 to test anothercondition of the frequency domain waveform, proceed to step 3450 and theimpact can be considered validated, or proceed to step 3410 to analyzethe time domain waveform (not shown by arrow).

At step 3438, the received data can be analyzed in the frequency-domainto determine whether the amplitudes within a specified range exceed afirst threshold, thereby rendering the received data unusable todetermine first and/or second modal frequencies. This can be determined,for example, by identifying a range of frequencies and finding the lowerquartile of amplitudes within that range. If the lower quartile ofamplitudes are above the first threshold, the condition at step 3438 isnot satisfied. Consequently, the impact fails validation (step 3440) andthe method is ended. If the lower quartile of amplitudes are below thefirst threshold, the condition at step 3438 is satisfied. Additionally,a second threshold, which is lower than the first threshold, can be setto adjust the confidence level if it is exceeded. For example, althoughthe amplitudes within the specified range may not have exceeded thefirst threshold and therefore the condition at step 3438 is satisfied,the amplitudes within the specified range may still be large enough tocall into question the accuracy of the data. Thus, if the amplitudesexceed the second threshold, the confidence level can be adjusted from 1to 0.5 (or kept at 0.5 if previously adjusted). Because the condition atstep 3438 was satisfied, the method can proceed to step 3450 and theimpact can be considered validated, or it can proceed to step 3410 toanalyze the time domain waveform (not shown by arrow).

Once the impact is considered validated at step 3450, the method canreturn information at step 3452 (e.g., information relating to the timedomain representation of the impact data, information relating to thefrequency domain representation of the impact data, confidence levels,value for F1 (if found when conditions were tested), etc.) and themethod is ended. It should be noted that any or all of the conditionsillustrated in FIG. 34 can be analyzed when carrying out method 3400.Moreover, the conditions analyzed can be analyzed in any order. Forexample, the condition at step 3414 can be analyzed, followed by thecondition at step 3438, followed by the condition at step 3412, etc.

FIG. 39 is a flow diagram illustrating a general method for determiningwhether an impact is valid. The method of FIG. 39 begins at step 3902with data being received from a sensor, such as an accelerometer,resulting from impacting a cantilever of a post-tensioned rod. At step3904, an initial confidence level corresponding to the impact can beset, for example, to a level of 1. At step 3906, the received data canbe analyzed to determine whether a first condition is met including, forexample, any of the conditions illustrated and described in connectionwith FIG. 34 . At step 3908, it can be determined whether the conditionis satisfied. If the condition is not satisfied, the impact failsvalidation (step 3910) and the method is ended at step 3920. If thecondition is satisfied, it can be determined at step 3912 whether thedata should be analyzed for another condition. If another condition isto be considered, the method repeats at step 3906 for the nextcondition. If no other conditions are to be considered, the impactpasses validation (step 3914) and data from the impact, the confidencelevel, and the value for F1 (if determined) are returned (step 3916).The method is ended at step 3920.

Determining F2. As discussed above in connection with step 3312 of themethod of FIG. 33 , a value for the second modal frequency (F2) can bedetermined from the data received from an accelerometer. There areseveral ways to determine F2. One example is the method of FIG. 40 .

FIG. 40 is a flow diagram illustrating an example method for determininga second modal frequency. The method begins at step 4002 by receivingdata from a sensor, such as an accelerometer, resulting from impacting acantilever of a post-tensioned rod, the confidence level associated withthe impact, and a value for F1 (if known). At step 4004, the receiveddata can be analyzed to identify a frequency with the highest amplitudein a specified frequency range. The specified range can be, for example,a frequency range that is known to likely contain a second modalfrequency for the rod. For example, the frequency range can beapproximately 3.9 to 6 times the frequency of F1. It should be notedthat if the value of F1 was not previously determined, it can bedetermined at this step. The frequency with the highest amplitude in thespecified range is assigned as the current value for F2.

At step 4006, the received data can be analyzed in the frequency domainto determine whether peak values at frequencies corresponding to wholeor half multiples of F1 exist, such as, for example, at 1.5 times F1 andat 2 times F1. If it is determined at step 4008 that peak values do notexist at whole or half multiples of F1, the current value for F2 can beassigned as the final value for F2 at step 4010. If it is determined atstep 4008 that peak values at whole or half multiples of F1 exist, it isdetermined at step 4014 whether the current value for F2 is a whole orhalf multiple of F1. For example, the current value for F2 can beanalyzed to determine if it is 4.5 times F1 or 5 times F1. If thecurrent value for F2 is not a whole or half multiple of F1, the currentvalue for F2 can be assigned as the final value for F2 at step 4010. Ifthe current value for F2 is a whole or half multiple of F1, theamplitude at the current value for F2 can be set to zero (step 4016) andthe confidence level can be set to 0 (step 4018). The confidence levelcan be set to 0 because the current value for F2 is discarded at step4016, indicating that the next value for F2 could be incorrect.

At step 4020, the received data is analyzed again in the specified rangeto identify a frequency with the highest amplitude, which is assigned asthe current value for F2. At step 4014, the current value of F2 isanalyzed to determine whether it is a whole or half multiple of F1. Thisprocess can be repeated until the current value of F2 is not a whole orhalf multiple of F1. When the final value of F2 is set at step 4010,data from the impact, values for F1 and F2, and the confidence level arereturned at step 4012. The method is ended at step 4030.

Data validation. As discussed above in connection with step 3320 of themethod of FIG. 33 , a data set comprising the stored data (e.g., impactdata, F1, F2, confidence levels, related data) can be validated. Thereare different ways to validate the data set. One example is the methodof FIG. 41 .

FIG. 41 is a flow diagram illustrating an example method for validatinga data set. The method begins at step 4102 by receiving the data set. Asnoted above, the data set can include values for F1, F2, and confidencelevels associated with each of the impacts. At step 4104, the values ofF2 can be grouped into unique groups. At step 4106, outlier values forF2 can be removed from each unique group. At step 4108, it is determinedwhether any of the unique groups contains a minimum number of F2 values,for example, at least five values. If none of the unique groups containsa minimum number of F2 values, the data set fails validation (step 4110)and the method is ended at step 4130.

If it is determined at step 4108 that at least one group contains aminimum number of F2 values, an optimum group can be found at step 4112.It should be noted that if only one group contains a minimum number ofF2 values, that group will be the optimum group. If more than one groupcontains a minimum number of F2 values, the optimum group could be, forexample, the group having the highest confidence levels.

At step 4114, the optimum group can be analyzed to determine if it meetsa certain threshold. For example, the optimum group can be analyzed todetermine if there are at least five F2 values, and that either one F2value has the highest confidence level or at least five F2 values havethe next highest confidence level. For example, where confidence levelscomprise 1, 0.5, and 0, it can be determined at step 4114 whether thereare at least five F2 values where at least one of the values has aconfidence level of 1, or whether there are at least five F2 valueswhere at least five of the values have a confidence level of 0.5. If theoptimum group does not meet the threshold, the data set fails validation(step 4110) and the method is ended at step 4130.

If the optimum group meets the threshold, the average of all F2 valueswithin the group can be determined at step 4116. At step 4118, outliervalues for F1 can be removed from the data set. At step 4120, theaverage of all remaining F1 values within the data set can bedetermined. The data set passes validation (step 4122) and the averagevalues of F1 and F2 are returned at step 4124. The method is ended atstep 4130.

Unique Groups. As discussed above in connection with step 4104 of themethod of FIG. 41 , the values of F2 can be grouped into unique groups.There are several ways to group values of F2 into unique groups. Oneexample is the method of FIG. 42 .

FIG. 42 is a flow diagram illustrating an example method for groupingvalues of F2 into unique groups. The method begins at step 4202 byreceiving values for F2. At step 4204, a bin window can be defined foreach value of F2. For example, a bin window can comprise a frequencyrange spanning from F2 to a value of F2 plus a frequency differential,such as 50 Hz. In this regard, each value of F2 will have its own binwindow. At step 4206, groups of values for F2 can be defined. Forexample, a group can be defined as all values of F2 that fall withineach bin window. At step 4208, groups that are fully encompassed withinanother group can be discarded. In this regard, the groups of F2 valuesat step 4210 will comprise unique groups of values for F2. The methodends at step 4212.

Removing Outliers. As discussed above in connection with steps 4106 and4118 of the method of FIG. 41 , outlier values of F2 and F1,respectively, can be removed. There are several ways to define anoutlier and to remove them. One example is the method of FIG. 43 .

FIG. 43 is a flow diagram illustrating an example method for removingoutlier values of F1 and/or F2. The method begins at step 4302 byreceiving groups of values for F1 or F2, such as, for example, uniquegroups of F2. At step 4304, it is determined whether the first groupcontains a minimum number of values, for example, at least five values.If the group does not contain a minimum number of values, the group canbe discarded at step 4306 and it can be determined, at step 4312,whether there are additional groups to consider. If there are additionalgroups to consider, the next group can be analyzed at step 4304 todetermine whether it contains a minimum number of values and the processcan be repeated.

If, at step 4304, the group being considered is determined to contain aminimum number of values, outlier values can be removed from the groupat step 4308. An outlier can be defined, for example, as a value greaterthan five standard deviations away from an average of the other valuesin the group. At step 4310, it can be determined whether the group beingconsidered still has a minimum number of values, for example, at leastfive values, after outliers were removed in step 4308. If the group doesnot contain a minimum number of values, the group can be discarded atstep 4306 and it can be determined, at step 4312, whether there areadditional groups to consider.

If it is determined at step 4310 that the group being considered has aminimum number of values, it can be determined at step 4312 whetherthere are additional groups to consider and the process described abovecan be repeated. If it is determined at step 4312 that there are noadditional groups to consider, groups fully encompassed by another groupcan be discarded at step 4316 and the groups of frequency values (F1 orF2) can be returned at step 4318. The method is ended at step 4320.

It will be appreciated that when the method of FIG. 43 is applied toonly one received group, such as a group of F1 values, and it isdetermined at step 4304 that the group does not contain a minimum numberof values, the group will be discarded at step 4306 and no additionalgroups will remain. In that case, no groups will be fully encompassed byanother group at step 4316. Accordingly, no groups will be returned atstep 4318. When the method of FIG. 43 is applied in connection with step4106 of the method of FIG. 41 , the data set will fail validationbecause, at step 4108, no group will contain a minimum number of values.

Optimum Group. As discussed above in connection with step 4112 of themethod of FIG. 41 , an optimum group of F2 values can be found. Thereare several ways to define and find an optimum group. One example is themethod of FIG. 44 .

FIG. 44 is a flow diagram illustrating an example method for finding anoptimum group of F2 values. The method begins at step 4402 by receivinggroups of F2 values, such as unique groups. At step 4404, the sum ofconfidence levels for each group can be computed. At step 4406, it isdetermined whether more than one group has the same highest confidencesum (i.e., a tie). If only one group has the highest confidence sum,that group is the optimum group and is returned at step 4408. The methodis ended at step 4410.

If more than one group has the same highest confidence sum, the numberof the highest confidence levels in each group can be determined at step4412. For example, where confidence levels comprise 1, 0.5, and 0, atstep 4412, the number of 1s for each group can be determined. At step4414, it is determined whether more than one group has the same numberof highest confidence levels. If only one group has the most highestconfidence levels, that group is the optimum group and is returned atstep 4416. The method is ended at step 4418.

If more than one group has the same number of highest confidence levels,the amount of F2 values in each group can be determined at step 4420. Atstep 4422, it is determined whether more than one group has the samenumber of F2 values. If only one group has the most F2 values, thatgroup is the optimum group and is returned at step 4424. The method isended at step 4426.

If more than one group has the same number of F2 values, determining theoptimum group is inconclusive (step 4428) and the method is ended atstep 4430.

While particular embodiments have been shown and described, it will beapparent to those skilled in the art that various changes andmodifications in form and details may be made therein without departingfrom the spirit and scope of this disclosure and are intended to form apart of the invention as defined by the following claims, which are tobe interpreted in the broadest sense allowable by law. For example,while many of the embodiments and the principles of the inventions havebeen explained in the context of first and second modal frequencies ofpost-tensioned rods, it is contemplated herein that other modalfrequencies may be used as well. Further, the sequence of steps for theexample methods described or illustrated herein are not to be construedas necessarily requiring their performance in the particular orderdescribed or illustrated unless specifically identified as requiring soor clearly identified through context. Moreover, the example methods mayomit one or more steps described or illustrated, or may includeadditional steps in addition to those described or illustrated. Thus,one of ordinary skill in the art, using the disclosures provided herein,will appreciate that various steps of the example methods can beomitted, rearranged, combined, and/or adapted in various ways withoutdeparting from the spirit and scope of the inventions.

What is claimed is:
 1. A system for estimating tension in apost-tensioned rod, the system comprising: an impact device fortransversely-impacting a post-tensioned rod; an accelerometer configuredto generate data indicative of a vibrational response in thepost-tensioned rod; and a receiver communicatively coupled to theaccelerometer, wherein the receiver comprises: a display; at least oneinput device; a communication module; a processor; and one or morememory devices coupled to the processor, wherein the one or more memorydevices stores instructions that, when executed by the processor, causethe processor to: receive the data indicative of a vibrational responsein the post-tensioned rod; process the received data to determine adifference between a first and a second modal frequency corresponding tothe vibrational response; and store the difference between a first andsecond modal frequency corresponding to the vibrational response;wherein the receiver is configured to transmit to an external system,via the communication module, the stored difference between a first andsecond modal frequency.
 2. A computing device for determining afrequency difference between a first and a second modal frequency of apost-tensioned rod, the computing device comprising: an input moduleconfigured to receive, from an accelerometer detachably coupled to apost-tensioned rod, data resulting from one or more impacts to acantilever portion of the post-tensioned rod; and a processor connectedto the interface and configured to: determine, for each of the one ormore impacts, that a second modal frequency can be determined from thereceived data; determine, from the received data, a value for the firstmodal frequency corresponding to each impact; determine, from thereceived data, a value for the second modal frequency corresponding toeach impact; determine, from at least the values for the first modalfrequency and the values for the second modal frequency, that afrequency difference can be determined for the values of the first andsecond modal frequencies; and determine the frequency difference betweenan average of the values for the first modal frequency and an average ofthe values for the second modal frequency.
 3. A non-transitory computerreadable medium including computer-executable instructions storedthereon, which, when executed by a processor, implement instructions fordetermining a frequency difference between a first and second modalfrequency of a post-tensioned rod, the instructions comprising:receiving, from an accelerometer detachably coupled to a post-tensionedrod, data resulting from one or more impacts to a cantilever portion ofthe post-tensioned rod; determining, for each of the one or more impact,that a second modal frequency can be determined from the received data;determining, from the received data, a value for the first modalfrequency corresponding to each impact; determining, from the receiveddata, a value for the second modal frequency corresponding to eachimpact; determining, from at least the values for the first modalfrequency and the values for the second modal frequency, that afrequency difference can be determined for the values of the first andsecond modal frequencies; and determining the frequency differencebetween an average of the values for the first modal frequency and anaverage of the values for the second modal frequency.